What is the L.C.M
of
a 8 and 12
b 16 and 20
c 21 and 18

To find the Least Common Multiple (L.C.M), we can use the prime factorization approach or the relationship between the Greatest Common Divisor (G.C.D) and L.C.M.

For 8 and 12, the prime factors are 2³ (for 8) and 2² × 3¹ (for 12). The L.C.M is calculated by taking the highest power of each prime: L.C.M = 2³ × 3¹ = 24.

For 16 and 20, the prime factors are 2⁴ (for 16) and 2² × 5¹ (for 20). The L.C.M here is 2⁴ × 5¹ = 80.

For 21 and 18, the factors are 3² (for 18) and 7¹ × 3¹ (for 21). Therefore, the L.C.M = 2⁰ × 3² × 7¹ = 126.

So, the L.C.M of each set is:
a) 24
b) 80
c) 126