Least Common Multiple (LCM) of 69 and 169
The least common multiple (LCM) of 69 and 169 is 11661.
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 69 and 169?
First, calculate the GCD of 69 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 169 = 0 remainder 69 |
| 2 | 169 ÷ 69 = 2 remainder 31 |
| 3 | 69 ÷ 31 = 2 remainder 7 |
| 4 | 31 ÷ 7 = 4 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 90 | 7740 |
| 101 and 185 | 18685 |
| 174 and 175 | 30450 |
| 200 and 50 | 200 |
| 151 and 103 | 15553 |