Least Common Multiple (LCM) of 71 and 169
The least common multiple (LCM) of 71 and 169 is 11999.
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 71 and 169?
First, calculate the GCD of 71 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 169 = 0 remainder 71 |
| 2 | 169 ÷ 71 = 2 remainder 27 |
| 3 | 71 ÷ 27 = 2 remainder 17 |
| 4 | 27 ÷ 17 = 1 remainder 10 |
| 5 | 17 ÷ 10 = 1 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 82 | 12382 |
| 129 and 93 | 3999 |
| 186 and 24 | 744 |
| 139 and 74 | 10286 |
| 41 and 119 | 4879 |