Find the LCM of 24 and 90 using prime factorisation.

Class 6Playing with NumbersPlaying with Numbers

A6
B360
C2,160
D60

Step-by-Step Solution

24 =

2 \times 2 \times 2 \times 3

and

90 = 2 \times 3 \times 3 \times 5

. Take each prime the greater number of times:

2 \times 2 \times 2 \times 3 \times 3 \times 5 = 360

. The traps:

6 = 2 \times 3

is the HCF, and 2,160 is simply

24 \times 90

— the product equals the LCM only when the two numbers are co-prime, and these share 2 and 3.

Answer: B) 360

Key idea: Prime vs composite

A whole number greater than 1 is **prime** if it has exactly two factors: 1 and itself. It is **composite** if it has more than two factors. The number 1 is neither prime nor composite (it has only one factor — itself). 2 is the only **even** prime; every other even number is divisible by 2 and so has at least three factors.

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