{"id":5312,"date":"2021-12-05T12:13:03","date_gmt":"2021-12-05T12:13:03","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=5312"},"modified":"2022-01-02T07:25:38","modified_gmt":"2022-01-02T07:25:38","slug":"lcm-of-fractions-with-examples-and-faq-mindspark","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/lcm-of-fractions-with-examples-and-faq-mindspark\/","title":{"rendered":"LCM of Fractions With Examples and FAQ – Mindspark"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
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LCM of Fractions With Examples and FAQ – Mindspark<\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

How to Find LCM of Fractions<\/b><\/b><\/h2>\n

<\/b><\/p>\n

LCM is the smallest common multiple of the given numbers. HCF is the largest number, which divides the given numbers completely.\u00a0<\/span><\/b><\/span><\/p>\n

LCM of fractions will be the smallest fraction that is a multiple of the given fractions. To calculate it, we use the formula given below –\u00a0<\/span><\/p>\n

<\/b>LCM of fractions = (LCM of all the numerators)\/(HCF of all the denominators)<\/span><\/span><\/p>\n

Let us understand this using a mathematical problem.\u00a0<\/span><\/p>\n

Example- Find the LCM of \\frac{2}{3} \\text{ and } \\frac{3}{5}<\/span>.<\/b><\/p>\n

As we know the formula,<\/span><\/p>\n

LCM of the fractions = (LCM of all the numerators)\/(HCF of all the denominators)<\/span><\/p>\n

Here the numerators are 2 and 3; denominators are 3 and 5.<\/span><\/p>\n

LCM of numerators (2 and 3) = 6<\/span><\/p>\n

HCF of denominators (3 and 5) = 1<\/span><\/p>\n

Now, we will put these values in the formula of fractions.<\/span><\/p>\n

We get, LCM of \\frac{2}{3} \\text{ and } \\frac{3}{5}<\/span>= (LCM of 2, 3)\/(HCF of 3, 5)<\/span><\/p>\n

So, LCM of \\frac{2}{3} \\text{ and } \\frac{3}{5} = \\frac{6}{1} = 6<\/span><\/span><\/p>\n

<\/span><\/p>\n

Similarly, we can find LCM of three or more fractions also. Let us see an example.<\/span><\/span><\/p>\n

Example- Find the LCM of \\frac{1}{2} ,\\frac{5}{6}\\text{ and } \\frac {7}{8}<\/span>.<\/b><\/p>\n

Now we have three numerators – 1, 5, and 7<\/span><\/p>\n

And also three denominators – 2, 6, and 8<\/span><\/p>\n

LCM of numerators (1, 5, 7) = 35<\/span><\/p>\n

HCF of denominators (2, 6, 8) = 2<\/span><\/p>\n

Now using the formula of LCM of fractions –<\/span><\/p>\n

LCM of \\frac{1}{2},\\frac{5}{6}\\text{ and }\\frac{7}{8}<\/span> = (LCM of 1, 5, 7) \/ (HCF of 2, 6, 8)<\/span><\/p>\n

So, LCM of \\frac{1}{2},\\frac{5}{6}\\text{ and }\\frac{7}{8}<\/span> =\\frac{35}{2}=17\\frac{1}{2}<\/span><\/span><\/p>\n

 <\/p>\n

Examples<\/b><\/h2>\n

<\/b><\/p>\n

1. What is the LCM of \\frac{3}{4} \\text{ and }\\frac{1}{3}<\/span>?<\/span><\/h3>\n

LCM of the fractions = (LCM of all the numerators)\/(HCF of all the denominators)<\/span><\/p>\n

Here the numerators are 3 and 1.<\/span><\/p>\n

The LCM of 3 and 1 will be 3.<\/span><\/p>\n

The denominators are 4 and 3<\/span><\/p>\n

The HCF of 4 and 3 will be 1.<\/span><\/p>\n

So,<\/span><\/p>\n

LCM of \\frac{3}{4}\\text{ and } \\frac{1}{3}<\/span>= (LCM of 3, 1) \/ (HCF of 4, 3)<\/span><\/p>\n

Therefore, LCM of \\frac{3}{4} \\text{ and }\\frac{1}{3}= \\frac{3}{1} = 3<\/span><\/span><\/p>\n

<\/b><\/p>\n

2. What is the LCM of \\frac{1}{2},\\frac{5}{6}\\text{ and }\\frac{15}{8}<\/span>?<\/span><\/h3>\n

LCM of fractions = (LCM of all the numerators)\/(HCF of all the denominators)<\/span><\/p>\n

Here the numerators are 1, 5 and 15.<\/span><\/p>\n

LCM of 1, 5 and 15 will be 15.<\/span><\/p>\n

The denominators are 2, 6 and 8<\/span><\/p>\n

HCF of 2, 6 and 8 will be 2.<\/span><\/p>\n

So,<\/span><\/p>\n

LCM of <\/span>\\frac{1}{2},\\frac{5}{6}\\text{ and }\\frac{15}{8}<\/span><\/span><\/p>\n

= (LCM of 1, 5, 15) \/ (HCF of 2, 6, 8)<\/span><\/p>\n

Therefore, LCM of <\/span>\\frac{1}{2},\\frac{5}{6}\\text{ and }\\frac{15}{8}<\/span><\/span><\/p>\n

= \\frac{15}{2}=7\\frac{1}{2}<\/span><\/span><\/p>\n

<\/span><\/p>\n

<\/span><\/p>\n

[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics
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Explore Other Topics<\/h1>\n

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\n
Geometry<\/a><\/div>\n
Trigonometry<\/a><\/div>\n
Operations<\/a><\/div>\n
Numbers<\/a><\/div>\n<\/div>\n

[\/et_pb_text][et_pb_text admin_label=”Related Concepts
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Related Concepts<\/h1>\n

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\n
Types of fractions<\/a><\/div>\n
Unlike Fractions<\/a><\/div>\n
LCM of two numbers<\/a><\/div>\n<\/div>\n

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Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
    <\/ol>\n

    Q1. How to find LCM of two fractions?<\/strong><\/h3>\n

    Ans: <\/strong>For finding the LCM (least common multiple) of two fractions, we have to use the below formula:
    LCM of two fractions = (LCM of the two numerators)\/(HCF of the two denominators).
    <\/strong><\/span><\/span><\/p>\n

    Q2. How to find the HCF?<\/strong><\/h3>\n

    Ans: <\/strong>First, list the factors of two numbers and then identify the common factors of the two numbers. HCF (highest common factor) of the two numbers is the highest factor among the common factors of the given numbers.

    <\/strong><\/p>\n

    [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

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