Least Common Multiple (LCM) of 137 and 167
The least common multiple (LCM) of 137 and 167 is 22879.
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 167?
First, calculate the GCD of 137 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 167 = 0 remainder 137 |
| 2 | 167 ÷ 137 = 1 remainder 30 |
| 3 | 137 ÷ 30 = 4 remainder 17 |
| 4 | 30 ÷ 17 = 1 remainder 13 |
| 5 | 17 ÷ 13 = 1 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 45 | 225 |
| 65 and 114 | 7410 |
| 168 and 120 | 840 |
| 186 and 48 | 1488 |
| 140 and 120 | 840 |