Least Common Multiple (LCM) of 137 and 74
The least common multiple (LCM) of 137 and 74 is 10138.
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 74?
First, calculate the GCD of 137 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 74 = 1 remainder 63 |
| 2 | 74 ÷ 63 = 1 remainder 11 |
| 3 | 63 ÷ 11 = 5 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 118 | 6726 |
| 116 and 133 | 15428 |
| 110 and 30 | 330 |
| 100 and 79 | 7900 |
| 195 and 26 | 390 |