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# What is the least positive integer which when divided by 2, 3, 4, 5 an

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What is the least positive integer which when divided by 2, 3, 4, 5 an [#permalink]
Bunuel wrote:
What is the least positive integer which when divided by 2, 3, 4, 5 and 6 leaves 1, 2, 3, 4 and 5 as remainders, respectively, but when divided by 7 leaves no remainder ?

(A) 109
(B) 119
(C) 126
(D) 154
(E) 210

Add one to this number, then if we divide by 2, 3, 4, 5, 6 it would leave no remainder. Hence this number plus 1, is a multiple of 2, 3, 4, 5, and 6.

The LCM of 2, 3, 4, 5, 6, is the LCM of 12, 5, and 6, which is 60. Then this number can be expressed as $$60*i - 1$$.

Our candidates are 59, 119, and 179. Normally we would check which of them is a multiple of 7 but only 119 is a possible choice.

Ans: B
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Re: What is the least positive integer which when divided by 2, 3, 4, 5 an [#permalink]
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We need to find What is the least positive integer which when divided by 2, 3, 4, 5 and 6 leaves 1, 2, 3, 4 and 5 as remainders, respectively, but when divided by 7 leaves no remainder

Number when divided by 2 gives 1 remainder

=> Number is odd
Only odd choices are A and B

Number when divided by 3 gives 1 remainder

Remainder of 109 when divided by 3 = Remainder of (1+0+9) when divided by 3 = Remainder of 10 when divided by 3 = 1 => FALSE