Least Common Multiple (LCM) of 108 and 141
The least common multiple (LCM) of 108 and 141 is 5076.
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 108 and 141?
First, calculate the GCD of 108 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 141 = 0 remainder 108 |
| 2 | 141 ÷ 108 = 1 remainder 33 |
| 3 | 108 ÷ 33 = 3 remainder 9 |
| 4 | 33 ÷ 9 = 3 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 18 | 936 |
| 121 and 138 | 16698 |
| 110 and 111 | 12210 |
| 160 and 62 | 4960 |
| 34 and 82 | 1394 |