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 :
In the question, we are asked smallest number which leaves remainder 7.
So, required number will be 7 more than LCM.
∴ Required number = LCM + 7
Now, finding the LCM of 12, 16, 24 & 36 by prime factorization method.
12 = 2 × 2 × 3
16 =2 × 2 × 2 × 2
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
∴ LCM = 2 × 2 × 2 × 2 × 3 × 3
= 16 × 9 = 144
So, required number = LCM + 7
= 144 + 7
= 151
The least number which when divided by 12,16,24 and 36 leaves a remainder 7 in each case is 151.
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