Least Common Multiple (LCM) of 75 and 67
The least common multiple (LCM) of 75 and 67 is 5025.
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 75 and 67?
First, calculate the GCD of 75 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 67 = 1 remainder 8 |
| 2 | 67 ÷ 8 = 8 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 82 | 2460 |
| 83 and 96 | 7968 |
| 13 and 61 | 793 |
| 190 and 33 | 6270 |
| 78 and 111 | 2886 |