Least Common Multiple (LCM) of 101 and 71
The least common multiple (LCM) of 101 and 71 is 7171.
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 71?
First, calculate the GCD of 101 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 71 = 1 remainder 30 |
| 2 | 71 ÷ 30 = 2 remainder 11 |
| 3 | 30 ÷ 11 = 2 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 103 | 6489 |
| 185 and 167 | 30895 |
| 123 and 40 | 4920 |
| 141 and 66 | 3102 |
| 80 and 143 | 11440 |