Least Common Multiple (LCM) of 120 and 49
The least common multiple (LCM) of 120 and 49 is 5880.
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 49?
First, calculate the GCD of 120 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 49 = 2 remainder 22 |
| 2 | 49 ÷ 22 = 2 remainder 5 |
| 3 | 22 ÷ 5 = 4 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 143 | 8151 |
| 28 and 29 | 812 |
| 65 and 87 | 5655 |
| 177 and 11 | 1947 |
| 42 and 65 | 2730 |