Least Common Multiple (LCM) of 120 and 144
The least common multiple (LCM) of 120 and 144 is 720.
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 144?
First, calculate the GCD of 120 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 144 = 0 remainder 120 |
| 2 | 144 ÷ 120 = 1 remainder 24 |
| 3 | 120 ÷ 24 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 72 | 12024 |
| 190 and 164 | 15580 |
| 78 and 85 | 6630 |
| 150 and 167 | 25050 |
| 50 and 115 | 1150 |