Least Common Multiple (LCM) of 43 and 157
The least common multiple (LCM) of 43 and 157 is 6751.
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 43 and 157?
First, calculate the GCD of 43 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 157 = 0 remainder 43 |
| 2 | 157 ÷ 43 = 3 remainder 28 |
| 3 | 43 ÷ 28 = 1 remainder 15 |
| 4 | 28 ÷ 15 = 1 remainder 13 |
| 5 | 15 ÷ 13 = 1 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 175 | 26075 |
| 152 and 57 | 456 |
| 73 and 31 | 2263 |
| 127 and 82 | 10414 |
| 52 and 67 | 3484 |