
Shortcut Trick
The Least Common Multiple (LCM) follows the associative property, which states that LCM(A, B, C, D) = LCM[LCM(A, B), LCM(C, D)].
⇒ Given LCM(A, B) = 20 and LCM(C, D) = 30.
⇒ Required LCM = LCM(20, 30).
⇒ The smallest number divisible by both 20 and 30 is 60.
∴ The correct answer is 60.

Alternate Method
Given:
LCM of A and B = 20
LCM of C and D = 30
Formula Used:
LCM(a, b, c, d) = LCM(LCM(a, b), LCM(c, d))

Calculations:
⇒ We need to find the LCM of 20 and 30.
⇒ Prime factorization of 20 = 2 × 2 × 5 = 22 × 5
⇒ Prime factorization of 30 = 2 × 3 × 5
⇒ LCM is the product of the highest powers of all prime factors involved.
⇒ LCM = 22 × 3 × 5
⇒ LCM = 4 × 3 × 5 = 60
∴ The correct answer is 60.

Additional Information
Associative Property of LCM
The LCM of a set of numbers can be found by grouping them: LCM(a, b, c) = LCM(a, LCM(b, c)).
Relationship between HCF and LCM
For any two positive integers a and b: HCF(a, b) × LCM(a, b) = a × b.
LCM of Fractions
LCM of (a/b, c/d) = LCM of numerators (a, c) ÷ HCF of denominators (b, d).