Least Common Multiple (LCM) of 36 and 171
The least common multiple (LCM) of 36 and 171 is 684.
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 36 and 171?
First, calculate the GCD of 36 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 171 = 0 remainder 36 |
| 2 | 171 ÷ 36 = 4 remainder 27 |
| 3 | 36 ÷ 27 = 1 remainder 9 |
| 4 | 27 ÷ 9 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 70 | 9730 |
| 57 and 109 | 6213 |
| 145 and 24 | 3480 |
| 73 and 105 | 7665 |
| 113 and 13 | 1469 |