Least Common Multiple (LCM) of 111 and 169
The least common multiple (LCM) of 111 and 169 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 111 and 169?
First, calculate the GCD of 111 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 169 = 0 remainder 111 |
| 2 | 169 ÷ 111 = 1 remainder 58 |
| 3 | 111 ÷ 58 = 1 remainder 53 |
| 4 | 58 ÷ 53 = 1 remainder 5 |
| 5 | 53 ÷ 5 = 10 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 56 | 3304 |
| 103 and 160 | 16480 |
| 78 and 164 | 6396 |
| 75 and 39 | 975 |
| 28 and 93 | 2604 |