Determine the number nearest 110000 but greater than 100000 which is exactly divisible by each of 8, 15 and 21.

Updated on May 31, 2025 | By Learnzy Admin

Step 1: Find the Least Common Multiple (LCM) of 8, 15, and 21.

Prime factorization:
8 = 2³
15 = 3 × 5
21 = 3 × 7
LCM = 2³ × 3 × 5 × 7 = 8 × 3 × 5 × 7 = 840

So, any number divisible by 8, 15, and 21 must be a multiple of 840.

Step 2: Find the multiple of 840 that is nearest to 110000 and greater than 100000.

Divide 110000 by 840:
110000 ÷ 840 ≈ 130.95
Now check nearby multiples:
130 × 840 = 109200
131 × 840 = 110040
132 × 840 = 110880

Among these, 110040 is the nearest to 110000 and is greater than 100000.

Hence answer is 110040

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