Find the least number which when divided by 6, 15, 18 leave remainder 5 in each case.

By Ritesh|Updated : November 11th, 2022

The least number which when divided by 6, 15, 18 leaves the remainder of 5 in each case is 95. Finding the smallest common multiple between any two or more numbers is done using the least common multiple (LCM) approaches. A number that is a multiple of two or more other numbers is said to be a common multiple.

Formula of LCM

Let a and b be two integers that are known. The following is the formula to determine the LCM of a and b:

LCM (a,b) = (a x b)/GCD(a,b)

GCD (a,b) refers to the greatest common factor or greatest common denominator of a and b.

Now we have to find the LCM of the given numbers:

The given numbers 6, 15, and 18 can be expressed as the prime factors

6 = 2 x 3

15 = 3 x 5

18 = 2 x 3 x 3

LCM (6, 15, 18) = 2 x 3 x 3 x 5

= 90

When the number that is 5 more than the LCM of the given numbers is divided by these numbers, 5 is a reminder. Therefore, the needed number is 90 + 5 = 95. Thus, 95 will be divided by the supplied numbers, leaving a leftover of 5, or 5.

Summary:

Find the least number which when divided by 6, 15, 18 leave remainder 5 in each case.

95 is the smallest number, and when divided by 6, 15, and 18, leaves a remainder of 5, in each instance. Division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in maths.

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