Least Common Multiple (LCM) of 138 and 76
The least common multiple (LCM) of 138 and 76 is 5244.
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 76?
First, calculate the GCD of 138 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 76 = 1 remainder 62 |
| 2 | 76 ÷ 62 = 1 remainder 14 |
| 3 | 62 ÷ 14 = 4 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 104 | 16120 |
| 10 and 199 | 1990 |
| 109 and 104 | 11336 |
| 23 and 14 | 322 |
| 175 and 69 | 12075 |