Least Common Multiple (LCM) of 120 and 165
The least common multiple (LCM) of 120 and 165 is 1320.
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 165?
First, calculate the GCD of 120 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 165 = 0 remainder 120 |
| 2 | 165 ÷ 120 = 1 remainder 45 |
| 3 | 120 ÷ 45 = 2 remainder 30 |
| 4 | 45 ÷ 30 = 1 remainder 15 |
| 5 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 75 | 12525 |
| 183 and 111 | 6771 |
| 105 and 176 | 18480 |
| 198 and 156 | 5148 |
| 61 and 64 | 3904 |