Least Common Multiple (LCM) of 120 and 162
The least common multiple (LCM) of 120 and 162 is 3240.
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 162?
First, calculate the GCD of 120 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 162 = 0 remainder 120 |
| 2 | 162 ÷ 120 = 1 remainder 42 |
| 3 | 120 ÷ 42 = 2 remainder 36 |
| 4 | 42 ÷ 36 = 1 remainder 6 |
| 5 | 36 ÷ 6 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 177 | 2478 |
| 91 and 108 | 9828 |
| 171 and 176 | 30096 |
| 13 and 100 | 1300 |
| 79 and 140 | 11060 |