Least Common Multiple (LCM) of 138 and 72
The least common multiple (LCM) of 138 and 72 is 1656.
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 72?
First, calculate the GCD of 138 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 72 = 1 remainder 66 |
| 2 | 72 ÷ 66 = 1 remainder 6 |
| 3 | 66 ÷ 6 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 59 | 11682 |
| 112 and 56 | 112 |
| 75 and 53 | 3975 |
| 101 and 200 | 20200 |
| 23 and 138 | 138 |