Least Common Multiple (LCM) of 120 and 45
The least common multiple (LCM) of 120 and 45 is 360.
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 45?
First, calculate the GCD of 120 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 45 = 2 remainder 30 |
| 2 | 45 ÷ 30 = 1 remainder 15 |
| 3 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 121 | 4477 |
| 88 and 178 | 7832 |
| 31 and 111 | 3441 |
| 191 and 98 | 18718 |
| 177 and 34 | 6018 |