Least Common Multiple (LCM) of 169 and 108
The least common multiple (LCM) of 169 and 108 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 169 and 108?
First, calculate the GCD of 169 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 108 = 1 remainder 61 |
| 2 | 108 ÷ 61 = 1 remainder 47 |
| 3 | 61 ÷ 47 = 1 remainder 14 |
| 4 | 47 ÷ 14 = 3 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 178 | 6764 |
| 149 and 49 | 7301 |
| 150 and 114 | 2850 |
| 119 and 58 | 6902 |
| 64 and 90 | 2880 |