Least Common Multiple (LCM) of 45 and 175
The least common multiple (LCM) of 45 and 175 is 1575.
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 45 and 175?
First, calculate the GCD of 45 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 175 = 0 remainder 45 |
| 2 | 175 ÷ 45 = 3 remainder 40 |
| 3 | 45 ÷ 40 = 1 remainder 5 |
| 4 | 40 ÷ 5 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 120 | 17160 |
| 176 and 199 | 35024 |
| 62 and 39 | 2418 |
| 96 and 80 | 480 |
| 142 and 125 | 17750 |