Least Common Multiple (LCM) of 37 and 175
The least common multiple (LCM) of 37 and 175 is 6475.
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 37 and 175?
First, calculate the GCD of 37 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 175 = 0 remainder 37 |
| 2 | 175 ÷ 37 = 4 remainder 27 |
| 3 | 37 ÷ 27 = 1 remainder 10 |
| 4 | 27 ÷ 10 = 2 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 72 | 1224 |
| 100 and 74 | 3700 |
| 173 and 170 | 29410 |
| 55 and 117 | 6435 |
| 55 and 66 | 330 |