Least Common Multiple (LCM) of 101 and 171
The least common multiple (LCM) of 101 and 171 is 17271.
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 171?
First, calculate the GCD of 101 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 171 = 0 remainder 101 |
| 2 | 171 ÷ 101 = 1 remainder 70 |
| 3 | 101 ÷ 70 = 1 remainder 31 |
| 4 | 70 ÷ 31 = 2 remainder 8 |
| 5 | 31 ÷ 8 = 3 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 93 | 3069 |
| 17 and 189 | 3213 |
| 107 and 14 | 1498 |
| 149 and 142 | 21158 |
| 119 and 42 | 714 |