find the smallest number which when added by 5 is divisible by 12,14,18
Answers
12 = 2^2 * 3
14 = 2*7
18 = 2 * 3^2
l.c.m = 2^2 * 3^2 * 7 = 252
So,252 is the smallest number which is divisible by each of 12,14 and 18.
252-5 = 247
Hence 247 is the smallest number which when added by 5 is divisible by 12,14,18.
Hope it helps
Answer:
The smallest number which when added by 5 is divisible by 12,14,18 = 247
Step-by-step explanation:
To find,
The smallest number which when added by 5 is divisible by 12,14 and 18
Recall the concept
Least common multiple (LCM)
The LCM of two or more numbers is defined the smallest number which is divisible by the given numbers
Hence the smallest number divisible by 12,14, and 18 is the LCM(12,14 and 18)
To find LCM(12,14 and 18)
The prime factorization of 12 = 2×2×3 = 2²×3
The prime factorization of 14 = 2×7
The prime factorization of 18 = 2 ×3×3 = 2×3²
The LCM(12,14,18) = 2²×3²×7 = 252
The smallest number divisible by 12, 14, 18 = 252
∴ The smallest number which when added by 5 is divisible by 12,14,18 = LCM (12,14,18) - 5 = 252 -5 = 247
The smallest number which when added by 5 is divisible by 12,14,18 = 247
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