Least Common Multiple (LCM) of 137 and 54
The least common multiple (LCM) of 137 and 54 is 7398.
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 54?
First, calculate the GCD of 137 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 54 = 2 remainder 29 |
| 2 | 54 ÷ 29 = 1 remainder 25 |
| 3 | 29 ÷ 25 = 1 remainder 4 |
| 4 | 25 ÷ 4 = 6 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 122 | 1342 |
| 97 and 127 | 12319 |
| 34 and 94 | 1598 |
| 184 and 72 | 1656 |
| 126 and 174 | 3654 |