Least Common Multiple (LCM) of 75 and 167
The least common multiple (LCM) of 75 and 167 is 12525.
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 167?
First, calculate the GCD of 75 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 167 = 0 remainder 75 |
| 2 | 167 ÷ 75 = 2 remainder 17 |
| 3 | 75 ÷ 17 = 4 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 65 | 12480 |
| 45 and 141 | 2115 |
| 48 and 184 | 1104 |
| 185 and 120 | 4440 |
| 17 and 37 | 629 |