Least Common Multiple (LCM) of 137 and 42
The least common multiple (LCM) of 137 and 42 is 5754.
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 42?
First, calculate the GCD of 137 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 42 = 3 remainder 11 |
| 2 | 42 ÷ 11 = 3 remainder 9 |
| 3 | 11 ÷ 9 = 1 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 184 | 31096 |
| 19 and 68 | 1292 |
| 98 and 149 | 14602 |
| 84 and 103 | 8652 |
| 137 and 90 | 12330 |