Least Common Multiple (LCM) of 138 and 52
The least common multiple (LCM) of 138 and 52 is 3588.
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 52?
First, calculate the GCD of 138 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 52 = 2 remainder 34 |
| 2 | 52 ÷ 34 = 1 remainder 18 |
| 3 | 34 ÷ 18 = 1 remainder 16 |
| 4 | 18 ÷ 16 = 1 remainder 2 |
| 5 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 120 | 12120 |
| 190 and 121 | 22990 |
| 199 and 168 | 33432 |
| 184 and 19 | 3496 |
| 170 and 192 | 16320 |