Least Common Multiple (LCM) of 169 and 111
The least common multiple (LCM) of 169 and 111 is 18759.
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 111?
First, calculate the GCD of 169 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 111 = 1 remainder 58 |
| 2 | 111 ÷ 58 = 1 remainder 53 |
| 3 | 58 ÷ 53 = 1 remainder 5 |
| 4 | 53 ÷ 5 = 10 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 115 | 16560 |
| 106 and 47 | 4982 |
| 104 and 93 | 9672 |
| 54 and 37 | 1998 |
| 73 and 179 | 13067 |