Question

Find the Lcm using short division method
A. 36 and 70
B.4,24 and 21
C. 3,13 and 33
PLease answer it in a ful form.

Answer 1

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 arithemetic

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

Answer 2

Answer:

Using 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.

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