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Question
Find the greatest number consisting of 6 digits which is exactly divisible by 24, 15, 36?
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Solution
To find L.C.M. of 24, 15, 36
24 = 23 × 3
15 = 3 × 5
36 = 22 × 32
| Prime factors of 24, 15, 36 |
Greatest Exponents |
| 2 | 3 |
| 3 | 2 |
| 5 | 1 |
∴ L.C.M. = 23 × 32 × 51
= 8 × 9 × 5
= 360
If a number has to be exactly divisible by 24, 15, and 36, then it has to be divisible by 360. Greatest 6 digit number is 999999.
Common multiplies of 24, 15, 36 with 6 digits are 103680, 116640, 115520, …, 933120, 999720 with six digits.
∴ The greatest number consisting of 6 digits which is exactly divisible by 24, 15, 36 is 999720.
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