Question

The product of two numbers is 756 if hcf is 12 find the lcm

Answer 1

Given :-

There are two numbers.

The product of two numbers is 756.

HCF of the numbers is 12.

To Find :-

LCM of the numbers.

Formula Used :-

LCM × HCF = Product of given numbers

Solution :-

LCM × HCF = Product of given numbers

Product of Numbers = 756

HCF = 12

Putting values,

LCM × 12 = 756

Divide both sides by 12,

( LCM × 12 ) / 12 = 756 / 12

LCM = 63

Answer :-

So, the LCM of given two numbers is 63.

Learn More :-

Highest Common Factor (HCF) :-

As the name suggest, it is highest common factor of given numbers.

It means the largest number which divides the given numbers.

For example, HCF of 18 and 27 is 9 as 9 is the largest number which divides 18 and 27 both.

Lowest Common Multiple (LCM) :-

As the name suggest, it is lowest common multiple of given numbers.

It means the lowest number which is divisible by given numbers.

For example, LCM of 12 and 36 is 36 as 36 is lowest number which is divisible by 12 and 36 both.

Answer 2

Given : Product of two numbers is 756 and their H.C.F is 12

To Find : L.C.M. of the two numbers.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

Here

$\:$

• Product of two numbers (ab) = 756
• H.C.F of two numbers = 12

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❍ We've to find the L.C.M of the two numbers.

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As we know that :

$\:$

$\star \: \: \underline{\boxed{\sf\pink{Product \: of \: two \: numbers = L.C.M × H.C.F }}}$

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❍ Put the values in the formula and solve.

$\: \:$

$\sf:\implies \: product \: of \: two \: numbers \: = L.C.M \: \times H.C.F \\ \\ \\ \sf:\implies \: 756 = L.C.M \times 12 \\ \\ \\ \sf:\implies \: L.C.M = \cancel\frac{756}{12} \\ \\ \\\sf:\implies \: \underline{\boxed{\mathfrak\purple{L.C.M \: = 63}}} \: \bigstar$

$\:$

$\:$

$\sf\therefore{\underline{Hence, \: the \: L.C.M \: of \: the \: two \: numbers \: is \: \bold{63}}}$