Least Common Multiple (LCM) of 132 and 85
The least common multiple (LCM) of 132 and 85 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 85?
First, calculate the GCD of 132 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 85 = 1 remainder 47 |
| 2 | 85 ÷ 47 = 1 remainder 38 |
| 3 | 47 ÷ 38 = 1 remainder 9 |
| 4 | 38 ÷ 9 = 4 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 24 | 600 |
| 52 and 130 | 260 |
| 185 and 88 | 16280 |
| 14 and 152 | 1064 |
| 38 and 36 | 684 |