Least Common Multiple (LCM) of 32 and 67
The least common multiple (LCM) of 32 and 67 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 32 and 67?
First, calculate the GCD of 32 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 67 = 0 remainder 32 |
| 2 | 67 ÷ 32 = 2 remainder 3 |
| 3 | 32 ÷ 3 = 10 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 145 | 725 |
| 142 and 117 | 16614 |
| 123 and 64 | 7872 |
| 119 and 63 | 1071 |
| 130 and 61 | 7930 |