Least Common Multiple (LCM) of 47 and 154
The least common multiple (LCM) of 47 and 154 is 7238.
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 154?
First, calculate the GCD of 47 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 154 = 0 remainder 47 |
| 2 | 154 ÷ 47 = 3 remainder 13 |
| 3 | 47 ÷ 13 = 3 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 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 |
|---|---|
| 99 and 124 | 12276 |
| 81 and 36 | 324 |
| 109 and 54 | 5886 |
| 140 and 16 | 560 |
| 18 and 17 | 306 |