[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
\n” _builder_version=”4.11.3″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\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
<\/b><\/p>\n
Before coming to the relation between these two, let us have a quick recap of LCM and HCF.<\/span><\/p>\n <\/p>\n HCF is the highest common factor of the given numbers or the largest number, which divides the given numbers completely without leaving any remainder.<\/span><\/p>\n For example, t<\/span>o find the HCF of 6 and 10, we must find the largest number that can divide 6 and 10 wholly.<\/span><\/p>\n 6 is wholly divisible by 1, <\/span>2<\/b>, 3, and 6.<\/span><\/p>\n 10 is wholly divisible by 1, <\/span>2<\/b>, 5, and 10.<\/span><\/p>\n Here, 2 is the largest common number that can divide 6 and 10 altogether.\u00a0<\/span><\/p>\n So, the required HCF = 2.<\/span><\/p>\n <\/p>\n As the full form of LCM suggests, it is the least (smallest) common multiple of the given numbers.<\/span><\/p>\n For example, to find the LCM of 6 and 10, we will have to find the smallest common multiple of the given numbers.<\/span><\/p>\n The first five multiples of the number 6 are 6, 12, 18, 24, and <\/span>30<\/b>.<\/p>\n The first five multiples of the number 10 are 10, 20, <\/span>30<\/b>, 40, and 50.<\/span><\/p>\n 30 is the smallest number that is common in both.\u00a0<\/span><\/p>\n So, the LCM of the given numbers is 30.<\/span><\/p>\n <\/p>\n (i)<\/b> The product of HCF and LCM of two numbers is always equal to the product of the given numbers.<\/b><\/p>\n Means, (HCF \u00d7 LCM) of two numbers = Product of the numbers.<\/span><\/span><\/p>\n Example:<\/b>\u00a0 Let us verify the above relation by taking two numbers, 10 and 15.<\/span><\/p>\n Solution:<\/span><\/p>\n HCF of 10 and 15 = 5<\/span><\/p>\n LCM of 10 and 15 = 30<\/span><\/p>\n LCM \u00d7 HCF = 30 \u00d7 5 = 150<\/span><\/p>\n Product of the given numbers = 10 \u00d7 15 = 150<\/span><\/p>\n Hence, it is verified that HCF \u00d7 LCM of two numbers = Product of the numbers.<\/span><\/p>\n \u00a0<\/span>Note-<\/b> Remember that this rule is applicable only for two numbers. The product of HCF and LCM of three numbers is never equal to the product of the given numbers.<\/span><\/p>\n <\/p>\n (ii) For co-prime numbers, HCF is 1, and LCM is the product of the numbers.<\/b><\/b><\/p>\n Co-prime numbers are the pair of numbers whose common multiple is only and only 1.<\/span>\u00a0<\/span><\/p>\n Example:<\/b> Let us verify the above relation by taking co-prime numbers, 7 and 11.\u00a0<\/span><\/p>\n Solution:<\/span><\/p>\n HCF (7 and 11) = 1<\/span><\/p>\n LCM (7 and 11) = 77<\/span><\/p>\n Product of the given numbers = 7 \u00d7 11 = 77<\/span><\/p>\n Thus, we verified that the HCF of co-prime numbers is 1 and LCM = Product of the Numbers.<\/span><\/p>\n <\/p>\n <\/span><\/p>\n As per the property of HCF and LCM of two numbers-\u00a0<\/span><\/p>\n LCM \u00d7 HCF = Product of the numbers<\/span><\/p>\n Here, LCM = 80, HCF = 12\u00a0<\/span><\/p>\n So, 80 \u00d7 12 = 24 \u00d7 Other Number<\/span><\/p>\n Therefore, Other Number = (80 \u00d7 12) \/ 24 = 80\/2 = 40<\/span><\/p>\n <\/p>\n <\/span><\/p>\n According to the property, LCM of Co-prime Numbers = Product Of the Numbers.<\/span><\/p>\n So, LCM of Co-prime Numbers = 2021.<\/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 [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\nWhat is HCF (Highest Common Factor)?<\/b><\/h2>\n
What is LCM (Least Common Multiple)?<\/b><\/h2>\n
Relation of HCF and LCM<\/b><\/b><\/h2>\n
<\/h2>\n
Examples\u00a0<\/b><\/h2>\n
<\/span><\/h3>\n
1. The HCF of the two numbers is 12, and their LCM is 80. If one of the two numbers is 24, find the second number.<\/span><\/h3>\n
2. If the product of two co-prime numbers is 2021, find the LCM of the numbers.<\/span><\/h3>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nRelated Concepts<\/h1>\n