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 |
|---|---|
| 162 and 45 | 810 |
| 82 and 91 | 7462 |
| 187 and 166 | 31042 |
| 180 and 71 | 12780 |
| 102 and 56 | 2856 |