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Find the Least Number Which When Divides 35, 56 and 91 Leaves the Same Remainder 7 in Each Case. - Mathematics

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Find the least number which when divides 35, 56 and 91 leaves the same remainder 7 in each case.

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Solution

Least number which can be divided by 35, 56 and 91 is LCM of 35, 56 and 91.
Prime factorization of 35, 56 and 91 is:
35 = 5 × 7
56 = 23 × 7
91 = 7 × 13
LCM = product of greatest power of each prime factor involved in the numbers = 23 × 5 × 7 × 13 = 3640
Least number which can be divided by 35, 56 and 91 is 3640.
Least number which when divided by 35, 56 and 91 leaves the same remainder 7 is 3640 + 7 = 3647.
Thus, the required number is 3647.

Concept: Euclid’s Division Lemma
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