Least Common Multiple (LCM) of 60 and 162
The least common multiple (LCM) of 60 and 162 is 1620.
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 60 and 162?
First, calculate the GCD of 60 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 162 = 0 remainder 60 |
| 2 | 162 ÷ 60 = 2 remainder 42 |
| 3 | 60 ÷ 42 = 1 remainder 18 |
| 4 | 42 ÷ 18 = 2 remainder 6 |
| 5 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 153 | 28305 |
| 103 and 195 | 20085 |
| 108 and 183 | 6588 |
| 36 and 84 | 252 |
| 142 and 116 | 8236 |