Least Common Multiple (LCM) of 47 and 157
The least common multiple (LCM) of 47 and 157 is 7379.
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 47 and 157?
First, calculate the GCD of 47 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 157 = 0 remainder 47 |
| 2 | 157 ÷ 47 = 3 remainder 16 |
| 3 | 47 ÷ 16 = 2 remainder 15 |
| 4 | 16 ÷ 15 = 1 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 32 | 2784 |
| 128 and 21 | 2688 |
| 186 and 47 | 8742 |
| 174 and 128 | 11136 |
| 145 and 151 | 21895 |