Least Common Multiple (LCM) of 18 and 169
The least common multiple (LCM) of 18 and 169 is 3042.
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 18 and 169?
First, calculate the GCD of 18 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 169 = 0 remainder 18 |
| 2 | 169 ÷ 18 = 9 remainder 7 |
| 3 | 18 ÷ 7 = 2 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 61 | 9821 |
| 83 and 169 | 14027 |
| 136 and 73 | 9928 |
| 115 and 191 | 21965 |
| 114 and 184 | 10488 |