Least Common Multiple (LCM) of 47 and 101
The least common multiple (LCM) of 47 and 101 is 4747.
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 101?
First, calculate the GCD of 47 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 101 = 0 remainder 47 |
| 2 | 101 ÷ 47 = 2 remainder 7 |
| 3 | 47 ÷ 7 = 6 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 107 | 15729 |
| 131 and 186 | 24366 |
| 163 and 169 | 27547 |
| 139 and 125 | 17375 |
| 199 and 75 | 14925 |