Least Common Multiple (LCM) of 127 and 137
The least common multiple (LCM) of 127 and 137 is 17399.
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 127 and 137?
First, calculate the GCD of 127 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 137 = 0 remainder 127 |
| 2 | 137 ÷ 127 = 1 remainder 10 |
| 3 | 127 ÷ 10 = 12 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 82 | 5412 |
| 90 and 119 | 10710 |
| 140 and 120 | 840 |
| 160 and 97 | 15520 |
| 106 and 83 | 8798 |