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 |
|---|---|
| 171 and 138 | 7866 |
| 121 and 92 | 11132 |
| 118 and 85 | 10030 |
| 179 and 12 | 2148 |
| 152 and 83 | 12616 |