Least Common Multiple (LCM) of 175 and 60
The least common multiple (LCM) of 175 and 60 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 175 and 60?
First, calculate the GCD of 175 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 60 = 2 remainder 55 |
| 2 | 60 ÷ 55 = 1 remainder 5 |
| 3 | 55 ÷ 5 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 100 | 16700 |
| 180 and 83 | 14940 |
| 146 and 167 | 24382 |
| 153 and 119 | 1071 |
| 21 and 145 | 3045 |