Least Common Multiple (LCM) of 137 and 30
The least common multiple (LCM) of 137 and 30 is 4110.
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 30?
First, calculate the GCD of 137 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 30 = 4 remainder 17 |
| 2 | 30 ÷ 17 = 1 remainder 13 |
| 3 | 17 ÷ 13 = 1 remainder 4 |
| 4 | 13 ÷ 4 = 3 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 96 | 9312 |
| 100 and 123 | 12300 |
| 93 and 137 | 12741 |
| 182 and 122 | 11102 |
| 108 and 111 | 3996 |