Least Common Multiple (LCM) of 137 and 52
The least common multiple (LCM) of 137 and 52 is 7124.
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 137 and 52?
First, calculate the GCD of 137 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 52 = 2 remainder 33 |
| 2 | 52 ÷ 33 = 1 remainder 19 |
| 3 | 33 ÷ 19 = 1 remainder 14 |
| 4 | 19 ÷ 14 = 1 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 126 | 126 |
| 41 and 156 | 6396 |
| 172 and 102 | 8772 |
| 49 and 59 | 2891 |
| 43 and 178 | 7654 |