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 |
|---|---|
| 180 and 45 | 180 |
| 37 and 170 | 6290 |
| 94 and 176 | 8272 |
| 146 and 110 | 8030 |
| 121 and 60 | 7260 |