Least Common Multiple (LCM) of 60 and 175
The least common multiple (LCM) of 60 and 175 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 60 and 175?
First, calculate the GCD of 60 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 175 = 0 remainder 60 |
| 2 | 175 ÷ 60 = 2 remainder 55 |
| 3 | 60 ÷ 55 = 1 remainder 5 |
| 4 | 55 ÷ 5 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 147 | 9996 |
| 26 and 188 | 2444 |
| 179 and 119 | 21301 |
| 123 and 149 | 18327 |
| 144 and 10 | 720 |