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Find the least number which when divided by 6, 15, 18 leave remainder 5 in each case.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
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.
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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.
