Least Common Multiple (LCM) of 138 and 53
The least common multiple (LCM) of 138 and 53 is 7314.
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 138 and 53?
First, calculate the GCD of 138 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 53 = 2 remainder 32 |
| 2 | 53 ÷ 32 = 1 remainder 21 |
| 3 | 32 ÷ 21 = 1 remainder 11 |
| 4 | 21 ÷ 11 = 1 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 63 | 1071 |
| 108 and 126 | 756 |
| 96 and 20 | 480 |
| 90 and 186 | 2790 |
| 96 and 13 | 1248 |