Least Common Multiple (LCM) of 137 and 105
The least common multiple (LCM) of 137 and 105 is 14385.
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 105?
First, calculate the GCD of 137 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 105 = 1 remainder 32 |
| 2 | 105 ÷ 32 = 3 remainder 9 |
| 3 | 32 ÷ 9 = 3 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 67 | 5360 |
| 170 and 94 | 7990 |
| 36 and 56 | 504 |
| 101 and 133 | 13433 |
| 48 and 77 | 3696 |