Least Common Multiple (LCM) of 101 and 47
The least common multiple (LCM) of 101 and 47 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 101 and 47?
First, calculate the GCD of 101 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 47 = 2 remainder 7 |
| 2 | 47 ÷ 7 = 6 remainder 5 |
| 3 | 7 ÷ 5 = 1 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 21 | 2688 |
| 110 and 11 | 110 |
| 113 and 131 | 14803 |
| 48 and 175 | 8400 |
| 83 and 13 | 1079 |