Question

The HCF of two numbers is 12 and their product is 2160. Find
their LCM.

Answer 1

$\sf GivEn \begin{cases} & \sf{HCF\;of\;two\;numbers = \bf{12} } \\ & \sf{Product\;of\;two\;numbers = \bf{2160} } \end{cases}$

To find: LCM of these two numbers.

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☯ Let two numbers be a and b.

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$\dag\;{\underline{\frak{We\;know\;that,}}}$

• Relation between LCM and HCF of two numbers is,

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$\star\;{\boxed{\sf{\purple{LCM \times HCF = Product\;of\;two\;numbers}}}}$

Here,

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• HCF of two numbers a and b is 12
• Product of two numbers a and b is 2160

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$\dag\;{\underline{\frak{Putting\;values,}}}$

$:\implies\sf LCM \times 12 = 2160\\ \\ :\implies\sf LCM = \cancel{ \dfrac{2160}{12}}\\ \\ :\implies{\boxed{\frak{\pink{LCM = 180}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Thus,\;LCM\;of\;two\;numbers\;is\; {\textsf{\textbf{180}}}.}}}$

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$\qquad\qquad\boxed{\underline{\underline{\purple{\bigstar \: \bf\: More\:to\:know\:\bigstar}}}}$

• LCM (least common multiple) = LCM defines the least number which is exactly divisible by two or more numbers.
• LCM is also called the Least Common Divisor.

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• HCF (highest common factor) = HCF defines the greatest factor present in between given two or more numbers.
• H.C.F. is also called the greatest common factor (GCF).

Answer 2

Answer:

${\huge {\mathfrak { \blue {given}}}}$

• HCF of two numbers = 12
• Product of them = 2160

${\huge {\mathfrak { \blue {to \: find}}}}$

LCM of both number

${\huge {\mathfrak { \blue {solution}}}}$

${\small {\boxed { \green {{ \sf \star \: LCM \: \times HCF = product}}}}}$

Here,

HCF = 12

Product = 2160

$\sf \implies \: LCM \: \times HCF \: = product \:$

$\sf \implies LCM \: \times 12 = 2160$

$\sf \implies \: LCM \: = \dfrac{2160 }{12}$

$\sf \implies \: LCM \: = 180$

$\huge \fbox {LCM \: = 180}$

Let's verify

$\sf \implies \: LCM \times HCF \: = product$

$\sf \implies \: 180 \times 12 = 2160$

$\sf \implies \: 2160 = 2160$

Hence verified.

$\huge \bf \: learn \: more$

HCF - HCF is the Highest Common factor in any two numbers. It is also known GCD (Greatest common factor).

LCM - LCM is the lowest common multiple of any two numbers.