What is largest and smallest value divisible by 6, 15, 21 and 24 out of the 4…

To determine which values are divisible by 6, 15, 21, and 24, we must first find their Least Common Multiple (LCM). Any number divisible by all four must be a multiple of their LCM.

Step-by-Step Calculation
1. Find the LCM of 6, 15, 21, and 24:

Prime factorization:

6 = 2 * 3

15 = 3 * 5

21 = 3 * 7

24 = 2^3 * 3

To find the LCM, take the highest power of each prime factor present:

Factors: 2^3, 3, 5, 7

LCM = 8 * 3 * 5 * 7 = 840.

2. Evaluate the options:
A number is divisible by 6, 15, 21, and 24 if and only if it is a multiple of 840.

Option A: 9240, 840

840 / 840 = 1 (Divisible)

9240 / 840 = 11 (Divisible)

Option B, C, D: These contain numbers that are not multiples of 840 and therefore are not divisible by the given set.