Least Common Multiple (LCM) of 75 and 140
The least common multiple (LCM) of 75 and 140 is 2100.
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 140?
First, calculate the GCD of 75 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 140 = 0 remainder 75 |
| 2 | 140 ÷ 75 = 1 remainder 65 |
| 3 | 75 ÷ 65 = 1 remainder 10 |
| 4 | 65 ÷ 10 = 6 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 85 | 13260 |
| 93 and 173 | 16089 |
| 188 and 169 | 31772 |
| 120 and 47 | 5640 |
| 54 and 169 | 9126 |