Least Common Multiple (LCM) of 149 and 169
The least common multiple (LCM) of 149 and 169 is 25181.
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 149 and 169?
First, calculate the GCD of 149 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 169 = 0 remainder 149 |
| 2 | 169 ÷ 149 = 1 remainder 20 |
| 3 | 149 ÷ 20 = 7 remainder 9 |
| 4 | 20 ÷ 9 = 2 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 98 | 6370 |
| 179 and 30 | 5370 |
| 20 and 45 | 180 |
| 75 and 173 | 12975 |
| 81 and 32 | 2592 |