Find the least number which when divided by 12,15,18 and 36 leaves 10 as remainder.

11.

The difference between the greatest and least five-digit numbers formed by the digits 2, 5,0, 6, 8 is (repetition of digits are not allowed)

C.

65952

The difference five digit number formed by the digits 2, 5, 0, 6 and 8 = 86520The least five digit number formed by the digits 2, 5, 0, 6 and 8 = 20568

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We observe that 12 - 8 = 4, 18 - 14 = 4, 36 - 32 = 4 and 45 - 41 = 4

Hence, the required number should be LCM (12, 18, 36, 45) – 4

The LCM of 12, 18, 36 and 45 = 180.

Hence, required number = 180 – 4 = 176

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Find the smallest number which, when divided by 12, 15, 18, 24 and 36 leaves no remainder

The least number which is exactly divisible by each given number is their L.C.M. Required number L.C.M. of 12, 15, 18, 24 and 36.

∴ L.C.M. = Least required number
= 2 x 2 x 3 x 3 x 5 x 2 = 360

Hence, the least required number = 360

Concept: Property HCF x LCM = Product of Two Numbers

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