Least Common Multiple (LCM) of 47 and 152
The least common multiple (LCM) of 47 and 152 is 7144.
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 152?
First, calculate the GCD of 47 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 152 = 0 remainder 47 |
| 2 | 152 ÷ 47 = 3 remainder 11 |
| 3 | 47 ÷ 11 = 4 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 106 | 7526 |
| 189 and 63 | 189 |
| 31 and 96 | 2976 |
| 189 and 37 | 6993 |
| 163 and 39 | 6357 |