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 |
|---|---|
| 24 and 127 | 3048 |
| 144 and 170 | 12240 |
| 168 and 13 | 2184 |
| 160 and 188 | 7520 |
| 169 and 145 | 24505 |