Least Common Multiple (LCM) of 67 and 132
The least common multiple (LCM) of 67 and 132 is 8844.
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 67 and 132?
First, calculate the GCD of 67 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 132 = 0 remainder 67 |
| 2 | 132 ÷ 67 = 1 remainder 65 |
| 3 | 67 ÷ 65 = 1 remainder 2 |
| 4 | 65 ÷ 2 = 32 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 161 | 805 |
| 39 and 95 | 3705 |
| 51 and 86 | 4386 |
| 80 and 117 | 9360 |
| 38 and 22 | 418 |