Least Common Multiple (LCM) of 100 and 175
The least common multiple (LCM) of 100 and 175 is 700.
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 100 and 175?
First, calculate the GCD of 100 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 175 = 0 remainder 100 |
| 2 | 175 ÷ 100 = 1 remainder 75 |
| 3 | 100 ÷ 75 = 1 remainder 25 |
| 4 | 75 ÷ 25 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 132 | 264 |
| 124 and 175 | 21700 |
| 16 and 82 | 656 |
| 128 and 162 | 10368 |
| 13 and 54 | 702 |