Question by Summer Clouds - Discuss with MathYouLike

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14/09/2017 at 08:43

Namakshi wants to arrange her marching band in a rectangular array with the same number of band members in each row. But when she tried putting them in 3 rows, she had 1 band member left over; in 5 rows, she had 2 members left over; in 7 rows, she had 3 members left over; and in 9 rows, she had 4 members left over. What is the least number of members that could be in the band?

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Phan Thanh Tinh Coordinator 14/09/2017 at 10:45

Let x be the least number of members in the band, then x is divided by 3, 5, 7, 9 with remainders 1, 2, 3, 4 respecitvely.

Since 3 = 1.2 + 1 ; 5 = 2.2 + 1 ; 7 = 3.2 + 1 ; 9 = 4.2 + 1,

2x + 1 is divisible by 3 ; 5 ; 7 ; 9.

So, 2x + 1 = LCM(3,5,7,9) = 315 or x = 157

Hence, the answer is 157

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→இے๖ۣۜBoy™†hïếuGîa 16/09/2017 at 13:39

Let x be the least number of members in the band, then x is divided by 3, 5, 7, 9 with remainders 1, 2, 3, 4 respecitvely.

Since 3 = 1.2 + 1 ; 5 = 2.2 + 1 ; 7 = 3.2 + 1 ; 9 = 4.2 + 1,

2x + 1 is divisible by 3 ; 5 ; 7 ; 9.

So, 2x + 1 = LCM(3,5,7,9) = 315 or x = 157

Hence, the answer is 157

We need to

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