Least Common Multiple (LCM) of 116 and 53
The least common multiple (LCM) of 116 and 53 is 6148.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 116 and 53?
First, calculate the GCD of 116 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 53 = 2 remainder 10 |
| 2 | 53 ÷ 10 = 5 remainder 3 |
| 3 | 10 ÷ 3 = 3 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 135 | 7155 |
| 129 and 61 | 7869 |
| 77 and 51 | 3927 |
| 55 and 112 | 6160 |
| 103 and 67 | 6901 |