Question

LCM of 24 and 36 and HCF of 29 and 32
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Answer 1

Step-by-step explanation:

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: 24 and 36

Let us find the prime factorization of 24 and 36

24 = 2 × 2 × 2 × 3

24 = 23 × 3

36 = 2 × 2 × 3 × 3

36 = 22 × 3³

So,

HCF of (24, 36) = 2 × 2 × 3

HCF of (24, 36) = 12

LCM of (24, 36) = 2 × 2 × 3 × 2 × 3

LCM of (24, 36) = 72