Least Common Multiple (LCM) of 137 and 77
The least common multiple (LCM) of 137 and 77 is 10549.
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 77?
First, calculate the GCD of 137 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 77 = 1 remainder 60 |
| 2 | 77 ÷ 60 = 1 remainder 17 |
| 3 | 60 ÷ 17 = 3 remainder 9 |
| 4 | 17 ÷ 9 = 1 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 133 | 2926 |
| 54 and 89 | 4806 |
| 108 and 65 | 7020 |
| 107 and 143 | 15301 |
| 64 and 137 | 8768 |