Least Common Multiple (LCM) of 67 and 32
The least common multiple (LCM) of 67 and 32 is 2144.
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 32?
First, calculate the GCD of 67 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 32 = 2 remainder 3 |
| 2 | 32 ÷ 3 = 10 remainder 2 |
| 3 | 3 ÷ 2 = 1 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 124 | 6820 |
| 121 and 42 | 5082 |
| 198 and 82 | 8118 |
| 165 and 99 | 495 |
| 71 and 102 | 7242 |