Least Common Multiple (LCM) of 120 and 29
The least common multiple (LCM) of 120 and 29 is 3480.
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 29?
First, calculate the GCD of 120 and 29 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 29 = 4 remainder 4 |
| 2 | 29 ÷ 4 = 7 remainder 1 |
| 3 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 63 | 4095 |
| 180 and 81 | 1620 |
| 200 and 107 | 21400 |
| 23 and 153 | 3519 |
| 170 and 18 | 1530 |