Find the LCM of the following numbers in which one number is the factor of the other:

(a) 5, 20 (b) 6, 18 (c) 12, 48 (d) 9, 45

What do you observe in the result obtained?

The LCM of a number is the smallest number that is the product of two or more numbers.

A factor of a number is a number that divides the given number.

Answer: LCM of two numbers, where one is the factor of other, is the larger number.

Let's find the LCM of the given numbers in which one number is the factor of other and then observe the result.

Explanation:

The LCM can be found using diferent methods.

1. Using a formula of G.C.F , LCM(a,b) = (a×b) / GCF(a,b)
2. By multiplying prime factors with highest exponent factor.
3. List of Multiples

Let's find the LCM of the given numbers by multiplying prime factors with the highest exponent factor.

(a) 5, 20

Prime factorization of 5 is 5

Prime factorization of 20 is 2 × 2 × 5 = 2² × 5

Therefore, LCM (5, 20) = 2² × 5 = 4 × 5 = 20

(b) 6, 18

Prime factorization of 6 is 2 × 3

Prime factorization of 18 is 2 × 3 × 3 = 2 × 3²

Therefore, LCM (6, 18) = 2 × 3² = 2 × 9 = 18

(c) 12, 48

Prime factorization of 12 is 2 × 2 × 3

Prime factorization of 48 is 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

Therefore, LCM (12, 48) = 2⁴ × 3 = 16 × 3 = 48

(d) 9, 45

Prime factorization of 9 is 3 × 3

Prime factorization of 45 is 3 × 3 × 5 = 3² × 5

Therefore, LCM (9, 45) = 3² × 5 = 9 × 5 = 45

As per the results, we can observe that LCM of two numbers, where one is the factor of the other, is the other number only i.e. the larger number.

Thus, LCM of two numbers, where one is the factor of the other, is the larger number.