Least Common Multiple (LCM) of 138 and 65
The least common multiple (LCM) of 138 and 65 is 8970.
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 65?
First, calculate the GCD of 138 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 65 = 2 remainder 8 |
| 2 | 65 ÷ 8 = 8 remainder 1 |
| 3 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 135 | 7560 |
| 111 and 157 | 17427 |
| 146 and 22 | 1606 |
| 75 and 117 | 2925 |
| 102 and 191 | 19482 |