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HCF or the Highest Common Factor of two numbers is the largest number that can divide both the numbers. LCM or the Least Common Multiple is the smallest number that is evenly divisible by both the numbers. LCM is also known as Least Common Divisor. Now that we know what LCM and HCF are, how do we find two numbers when only their HCF and LCM are known?<\/span><\/p>\n Let us take any two numbers a, b, and let us say their HCF and LCM are s and y respectively. To find out the two numbers a and b, we must first understand the relationship between the two numbers and their HCF and LCM. <\/span>For any two numbers, the product of the two numbers is equal to the product of their HCF and LCM.\u00a0 <\/b>Let us take the example of 10 and 15. The HCF is 5 and the LCM is 30. Now, the product of the two numbers is <\/span>10\u271515 = 150<\/span>and this is equal to the product of the HCF and LCM which is <\/span>5 \u2715 30 = 150<\/span><\/p>\n Now that we have understood the relationship between the numbers and their HCF and LCM, we can find the two numbers by taking out the factors of the products of the HCF and LCM. We then eliminate the numbers which have a different HCF or LCM and any remaining pair is the number we are looking for. Note that there could be more than one pair of numbers that have the same HCF and LCM.<\/span><\/p>\n Taking the above example, let us find two numbers a and b, and their HCF is 5 while their LCM is 30.<\/span><\/p>\n Now we know that <\/span>a \u2715 b = 5\u271530 = 150<\/span><\/p>\n Let us factorize the product 150.<\/span><\/p>\n Factors of 150 are<\/span><\/p>\n 1 x 150,<\/span><\/p>\n 2 x 75,<\/span><\/p>\n 3 x 50,<\/span><\/p>\n 5 x 30,<\/span><\/p>\n 6 x 25, and<\/span><\/p>\n 10 x 15<\/span><\/p>\n We know that the HCF of the two numbers is 5. So we can eliminate (1, 150) (2,75) (3,50) (6,25) since their HCF is not 5. we are left with (5,30) and (10,15)\u00a0 and these are the two possible answers to this question.\u00a0<\/span><\/p>\n [\/et_pb_text][et_pb_text admin_label=”Sample Questions [\/et_pb_text][et_pb_text admin_label=”Question 1″ _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” custom_padding=”25px|25px|25px|25px|true|true” border_radii=”on|15px|15px|15px|15px” border_width_all=”2px” border_color_all=”#000000″ border_width_top=”4px” border_color_top=”#E02B20″ global_colors_info=”{}”]<\/p>\n Questions<\/strong><\/p>\n Solution:<\/b><\/p>\n Let y be the other number. We know that the product of the two numbers is equal to the product of the HCF and LCM of the numbers.\u00a0<\/span><\/p>\n So, <\/span>250 \u2715 y=750\u2715125<\/span><\/p>\n 250y=93750<\/span><\/p>\n y=375<\/span><\/p>\n Therefore, the other number is 375.<\/span><\/p>\n 2. The product of the two numbers is 765 and their HCF is 3. Find the LCM and the two numbers.<\/span><\/p>\n Solution:<\/b><\/p>\n Let a and b be the two numbers and y be the LCM.\u00a0<\/span><\/p>\n We know that the product of the two numbers equals the product of the HCF and LCM.\u00a0<\/span><\/p>\n i.e 765 = 3 X y<\/span><\/p>\n y = 255.<\/span><\/p>\n So the HCF and LCM of the two numbers are 3 and 255 respectively.\u00a0<\/span><\/p>\n Given that the product of the two numbers is 765.<\/span><\/p>\n The factors of 765 are\u00a0 (<\/span>1,765) (3,255)\u00a0 (5,153)\u00a0 (9,85) (15,51) (17,45)<\/span><\/p>\n Since the HCF of the two numbers is given as 3, that leaves only (3,255) and (15,51). These are two possible pairs of numbers whose LCM and HCF are 255 and 3 respectively.<\/span><\/p>\n<\/div>\n<\/div>\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=”http:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/7-days-week-free-trial.jpg” title_text=”7-days-week-free-trial” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.9.11″ _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=”4.10.6″ _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” hover_enabled=”0″ locked=”off” global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n<\/h2>\n
Finding two numbers when their HCF and LCM are given:<\/strong><\/h2>\n
\n” _builder_version=”4.10.8″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”28px” custom_padding=”|0px||4px|false|false” global_colors_info=”{}”]<\/p>\nPractice Multiple Choice Questions<\/h1>\n
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\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