<\/span><\/p>\n LCM of 8 and 12 is the smallest common multiple of 8 and 12. We have the following four methods to find the LCM of 8 and 12:\u00a0<\/span><\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n In this method, we will list the multiples of 8 and 12 until we find the first common multiple.<\/span><\/b><\/p>\n Multiples of 8 will be 8, 16, <\/span>24<\/b>, 32, 40, 48 etc.<\/span><\/p>\n Multiples of 12 will be: 12, <\/span>24<\/b>, 36, 48, 60, 72 etc.<\/span><\/b><\/p>\n Here, the number 24 (Bold ) is the first common multiple of both 8 and 12. So, the LCM of 8, 12 is 24.<\/span><\/p>\n <\/p>\n <\/span><\/p>\n In this find, we will list the prime factors of both numbers.<\/span><\/b><\/p>\n Prime factorization of:\u00a0<\/span><\/p>\n 8 = 2 \u00d7 2 \u00d7 2<\/span><\/p>\n 12 = 2 \u00d7 2 \u00d7 3<\/span><\/b><\/p>\n Now<\/span> List all the prime numbers found as they occur most times for any given number.\u00a0<\/span><\/p>\n The occurrence of Numbers:<\/span><\/p>\n 2: three times<\/span><\/p>\n 3: one time<\/span><\/p>\n Now, multiply the list of prime factors together to find the least common multiple (LCM).<\/span><\/p>\n So, the LCM of 8,12 = 2 \u00d7 2 \u00d7 2 \u00d7 3 = 24<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n Write down both the numbers (8 and 12) in the first row.\u00a0<\/span><\/b><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Begin with the Lowest Prime Number (2). If the numbers are not divisible by 2, we use the next prime number, i.e. 3. Divide the rows with 2 that evenly divides at least one of the numbers, and write the result into the next row.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n If any number is not divisible, write it down as it is.\u00a0<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Keep dividing, as explained earlier, till the last row is 1.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Now Multiply the prime numbers in the first column.<\/span><\/p>\n So the required LCM will be 2 \u00d7 2 \u00d7 2 \u00d7 3 = 24.<\/span><\/p>\n <\/span><\/p>\n <\/p>\n <\/b><\/p>\n The formula used to find the LCM by this method is:<\/span><\/p>\n L C M=\\frac{a \\times b} {H C F(a,b)}<\/span>\u00a0<\/span><\/p>\n HCF of 8 and 12 –\u00a0<\/span><\/p>\n 8 = <\/span>2 \u00d7 2 <\/span>\u00d7 2<\/span><\/p>\n 12 = <\/span>2 \u00d7 2 <\/span>\u00d7 3<\/span><\/p>\n 2 \u00d7 2 is common in the prime factorization of 8 and 12.<\/span><\/p>\n So, HCF = 2\u00d72 = 4<\/span><\/p>\n Now applying the value in the formula\u00a0<\/span><\/p>\n Required LCM\u00a0 =8 \\times\\frac{12}{4}=24<\/span><\/span><\/p>\n <\/span><\/p>\n <\/p>\n <\/p>\n <\/span><\/p>\n The smallest number completely divisible by 8 and 12 will be their LCM.<\/span><\/p>\n Multiples of 8 will be: 8, 16, 24, 32, 40, 48 etc.<\/span><\/p>\n Multiples of 12 will be: 12, 24, 36, 48, 60, 72 etc.<\/span><\/p>\n So the required LCM = smallest number completely divisible by 8 and 12 = 24<\/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 Given that LCM of 12 and 8 = 24<\/span><\/p>\n So, 24 \u00d7 HCF = 96<\/span><\/p>\n HCF = 96\/24 = 4<\/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 [\/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>\n\n
Listing Multiple Method<\/b><\/h2>\n
Prime Factorization Method<\/b><\/h2>\n
Division\/Ladder Method<\/b><\/h2>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/LCM-of-8-and-12-01.png\")
<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/LCM-of-8-and-12-02.png\")
<\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/LCM-of-8-and-12-03.png\")
<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/LCM-of-8-and-12-04.png\")
<\/span><\/p>\nHCF Method<\/b><\/h2>\n
Examples<\/b><\/h2>\n
1. Find the smallest number that is wholly divisible by 8 and 12.<\/span><\/h3>\n
2. If the LCM of the numbers 8 and 12 is 24, Find their HCF.<\/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