Least Common Multiple (LCM) of 120 and 175
The least common multiple (LCM) of 120 and 175 is 4200.
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 120 and 175?
First, calculate the GCD of 120 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 175 = 0 remainder 120 |
| 2 | 175 ÷ 120 = 1 remainder 55 |
| 3 | 120 ÷ 55 = 2 remainder 10 |
| 4 | 55 ÷ 10 = 5 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 48 | 192 |
| 110 and 50 | 550 |
| 200 and 14 | 1400 |
| 85 and 75 | 1275 |
| 80 and 20 | 80 |