Least Common Multiple (LCM) of 72 and 171
The least common multiple (LCM) of 72 and 171 is 1368.
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 72 and 171?
First, calculate the GCD of 72 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 171 = 0 remainder 72 |
| 2 | 171 ÷ 72 = 2 remainder 27 |
| 3 | 72 ÷ 27 = 2 remainder 18 |
| 4 | 27 ÷ 18 = 1 remainder 9 |
| 5 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 159 | 6042 |
| 155 and 91 | 14105 |
| 105 and 27 | 945 |
| 169 and 105 | 17745 |
| 43 and 101 | 4343 |