Least Common Multiple (LCM) of 137 and 67
The least common multiple (LCM) of 137 and 67 is 9179.
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 67?
First, calculate the GCD of 137 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 67 = 2 remainder 3 |
| 2 | 67 ÷ 3 = 22 remainder 1 |
| 3 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 41 | 2583 |
| 193 and 119 | 22967 |
| 29 and 77 | 2233 |
| 49 and 81 | 3969 |
| 135 and 42 | 1890 |