Least Common Multiple (LCM) of 137 and 46
The least common multiple (LCM) of 137 and 46 is 6302.
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 46?
First, calculate the GCD of 137 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 46 = 2 remainder 45 |
| 2 | 46 ÷ 45 = 1 remainder 1 |
| 3 | 45 ÷ 1 = 45 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 180 | 10980 |
| 189 and 21 | 189 |
| 140 and 105 | 420 |
| 17 and 42 | 714 |
| 80 and 129 | 10320 |