Least Common Multiple (LCM) of 137 and 78
The least common multiple (LCM) of 137 and 78 is 10686.
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 78?
First, calculate the GCD of 137 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 78 = 1 remainder 59 |
| 2 | 78 ÷ 59 = 1 remainder 19 |
| 3 | 59 ÷ 19 = 3 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 104 | 312 |
| 111 and 49 | 5439 |
| 52 and 48 | 624 |
| 190 and 26 | 2470 |
| 53 and 32 | 1696 |