Least Common Multiple (LCM) of 137 and 158
The least common multiple (LCM) of 137 and 158 is 21646.
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 158?
First, calculate the GCD of 137 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 158 = 0 remainder 137 |
| 2 | 158 ÷ 137 = 1 remainder 21 |
| 3 | 137 ÷ 21 = 6 remainder 11 |
| 4 | 21 ÷ 11 = 1 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 31 | 992 |
| 137 and 171 | 23427 |
| 106 and 45 | 4770 |
| 75 and 25 | 75 |
| 30 and 153 | 1530 |