Least Common Multiple (LCM) of 175 and 137
The least common multiple (LCM) of 175 and 137 is 23975.
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 137?
First, calculate the GCD of 175 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 137 = 1 remainder 38 |
| 2 | 137 ÷ 38 = 3 remainder 23 |
| 3 | 38 ÷ 23 = 1 remainder 15 |
| 4 | 23 ÷ 15 = 1 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 72 | 4392 |
| 17 and 80 | 1360 |
| 120 and 78 | 1560 |
| 170 and 170 | 170 |
| 109 and 29 | 3161 |