Find the least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case ?
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SOLUTION :
For this particular sum we need to find the LCM of the given numbers.
The smallest number which when divided by 12 16 24 and 36 = LCM of 12 16 24 and 36
12 = 2×2×3
16 = 2×2×2×2
24 = 2×2×2×3
36 = 2×2×3×3
LCM = 144
The smallest number which divides 12 16 24 and 36 is 144. But we have a condition that it leaves a remainder of 7. So we add 7 to the LCM (144+7=151).
Hence the smallest number that when divided by 12 16 24 and 36 leaves a remainder 7 is 151.
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