Least Common Multiple (LCM) of 137 and 168
The least common multiple (LCM) of 137 and 168 is 23016.
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 168?
First, calculate the GCD of 137 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 168 = 0 remainder 137 |
| 2 | 168 ÷ 137 = 1 remainder 31 |
| 3 | 137 ÷ 31 = 4 remainder 13 |
| 4 | 31 ÷ 13 = 2 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 200 | 4200 |
| 52 and 48 | 624 |
| 159 and 55 | 8745 |
| 49 and 48 | 2352 |
| 78 and 21 | 546 |