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Question
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is ______.
Options
10
100
504
2520
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Solution
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is 2520.
Explanation:
Factors of numbers from 1 to 10
1 = 1
2 = 1 × 2
3 = 1 × 3
4 = 1 × 2 × 2
5 = 1 × 5
6 = 1 × 2 × 3
7 = 1 × 7
8 = 1 × 2 × 2 × 2
9 = 1 × 3 × 3
10 = 1 × 2 × 5
∴ LCM of numbers from 1 to 10
= LCM(1, 2, 3, 4, 5, 6, 7, 8, 9,10)
= 1 × 2 × 2 × 2 × 3 × 3 × 5 × 7
= 2520
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