 # Find HCF and LCM of 336 and 54 by prime factorisation and verify that?

Highest Common Factor or HCF is the largest common divisor or gcd of two or more positive integers, as the mathematics rules dictate, appears to be the largest positive integer that divides the numbers without leaving a remainder.

Example:

Consider the two number 8 and 12.

As the highest number that can divide both 8 and 12 is 4.

Therefore, the H.C.F. of 8 and 12 would be 4.

In arithmetic, Least common multiple or LCM (a,b) is the least common multiple of two numbers, a and b. And the LCM is the smallest or least positive integer that is divisible by both a and b.

Example:

Consider the two number 8 and 12 and let us write the multiples of two numbers.

Multiples of 8 = 16, 24, 32, 40 ,48, 56……

Multiples of 12 = 24, 36, 48, 60, 72………

From the above list, we can observe that least common multiples of 8 and 12 is 24.

I.e LCM (8, 12) = 24

Given numbers: 336 and 54

Let us find the prime factorisation of 336 & 54.

336 = 2×2×2×2×3×7

336 = 2⁴ × 3 × 7

54 = 2×3×3×3

54 = 2 × 3³

So,

HCF of (336, 54) = 2 × 3

HCF of (336, 54) = 6

LCM of (336, 54) = 2⁴ × 3 × 7

LCM of (336, 54) = 3024

Now consider

Multiples of HCF and LCm is equal to the product of two numbers.

HCF × LCM × HCF = Product of two numbers.

6 × 3024 = 336 × 54

18144 = 18144