Least Common Multiple (LCM) of 137 and 175
The least common multiple (LCM) of 137 and 175 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 137 and 175?
First, calculate the GCD of 137 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 175 = 0 remainder 137 |
| 2 | 175 ÷ 137 = 1 remainder 38 |
| 3 | 137 ÷ 38 = 3 remainder 23 |
| 4 | 38 ÷ 23 = 1 remainder 15 |
| 5 | 23 ÷ 15 = 1 remainder 8 |
| 6 | 15 ÷ 8 = 1 remainder 7 |
| 7 | 8 ÷ 7 = 1 remainder 1 |
| 8 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 45 | 6390 |
| 111 and 106 | 11766 |
| 169 and 138 | 23322 |
| 164 and 53 | 8692 |
| 153 and 156 | 7956 |