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 |
|---|---|
| 136 and 87 | 11832 |
| 164 and 178 | 14596 |
| 165 and 94 | 15510 |
| 53 and 32 | 1696 |
| 37 and 16 | 592 |