Least Common Multiple (LCM) of 157 and 175
The least common multiple (LCM) of 157 and 175 is 27475.
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 157 and 175?
First, calculate the GCD of 157 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 175 = 0 remainder 157 |
| 2 | 175 ÷ 157 = 1 remainder 18 |
| 3 | 157 ÷ 18 = 8 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 59 | 59 |
| 101 and 195 | 19695 |
| 23 and 39 | 897 |
| 105 and 124 | 13020 |
| 30 and 111 | 1110 |