Least Common Multiple (LCM) of 120 and 149
The least common multiple (LCM) of 120 and 149 is 17880.
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 120 and 149?
First, calculate the GCD of 120 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 149 = 0 remainder 120 |
| 2 | 149 ÷ 120 = 1 remainder 29 |
| 3 | 120 ÷ 29 = 4 remainder 4 |
| 4 | 29 ÷ 4 = 7 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 135 | 5940 |
| 172 and 80 | 3440 |
| 181 and 24 | 4344 |
| 34 and 20 | 340 |
| 16 and 68 | 272 |