Least Common Multiple (LCM) of 75 and 118
The least common multiple (LCM) of 75 and 118 is 8850.
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 118?
First, calculate the GCD of 75 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 118 = 0 remainder 75 |
| 2 | 118 ÷ 75 = 1 remainder 43 |
| 3 | 75 ÷ 43 = 1 remainder 32 |
| 4 | 43 ÷ 32 = 1 remainder 11 |
| 5 | 32 ÷ 11 = 2 remainder 10 |
| 6 | 11 ÷ 10 = 1 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 158 | 6478 |
| 46 and 75 | 3450 |
| 101 and 67 | 6767 |
| 147 and 187 | 27489 |
| 72 and 84 | 504 |