Least Common Multiple (LCM) of 52 and 138
The least common multiple (LCM) of 52 and 138 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 52 and 138?
First, calculate the GCD of 52 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 138 = 0 remainder 52 |
| 2 | 138 ÷ 52 = 2 remainder 34 |
| 3 | 52 ÷ 34 = 1 remainder 18 |
| 4 | 34 ÷ 18 = 1 remainder 16 |
| 5 | 18 ÷ 16 = 1 remainder 2 |
| 6 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 66 | 990 |
| 25 and 22 | 550 |
| 164 and 174 | 14268 |
| 142 and 134 | 9514 |
| 154 and 168 | 1848 |