Least Common Multiple (LCM) of 132 and 170
The least common multiple (LCM) of 132 and 170 is 11220.
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 132 and 170?
First, calculate the GCD of 132 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 170 = 0 remainder 132 |
| 2 | 170 ÷ 132 = 1 remainder 38 |
| 3 | 132 ÷ 38 = 3 remainder 18 |
| 4 | 38 ÷ 18 = 2 remainder 2 |
| 5 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 136 | 680 |
| 107 and 85 | 9095 |
| 123 and 12 | 492 |
| 185 and 108 | 19980 |
| 129 and 41 | 5289 |