Least Common Multiple (LCM) of 108 and 169
The least common multiple (LCM) of 108 and 169 is 18252.
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 169?
First, calculate the GCD of 108 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 169 = 0 remainder 108 |
| 2 | 169 ÷ 108 = 1 remainder 61 |
| 3 | 108 ÷ 61 = 1 remainder 47 |
| 4 | 61 ÷ 47 = 1 remainder 14 |
| 5 | 47 ÷ 14 = 3 remainder 5 |
| 6 | 14 ÷ 5 = 2 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 131 | 8908 |
| 150 and 147 | 7350 |
| 112 and 115 | 12880 |
| 139 and 75 | 10425 |
| 85 and 97 | 8245 |