Find the least number exactly divisible by 12:15 20 and 27
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Answered by
51
Least number exactly divisible by 12, 15, 20 and 27 is the LCM of these 4 numbers.
12 = 2×2×3 = 2²×3
15 = 3×5
20 = 2×2×5 = 2²×5
27 = 3×3×3 = 3³
LCM = 2²×3³×5 = 540
Thus the least number exactly divisible by 12, 15, 20 and 27 is 540.
12 = 2×2×3 = 2²×3
15 = 3×5
20 = 2×2×5 = 2²×5
27 = 3×3×3 = 3³
LCM = 2²×3³×5 = 540
Thus the least number exactly divisible by 12, 15, 20 and 27 is 540.
Answered by
9
The least number is 540.
Step-by-step explanation:
We need to find the least number that is exactly divisible by 12,15,20 and 27
Firstly finding the prime factorization of 12,15,20 and 27 such that :
12 = 2×2×3
15 = 3×5
20 = 2×2×5
27 = 3×3×3
LCM is least common multiple. The LCM of above numbers is 540. Hence, 540 is the least number that is exactly divisible by 12,15,20 and 27.
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LCM
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