Least Common Multiple (LCM) of 116 and 169
The least common multiple (LCM) of 116 and 169 is 19604.
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 116 and 169?
First, calculate the GCD of 116 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 169 = 0 remainder 116 |
| 2 | 169 ÷ 116 = 1 remainder 53 |
| 3 | 116 ÷ 53 = 2 remainder 10 |
| 4 | 53 ÷ 10 = 5 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 103 | 19158 |
| 185 and 57 | 10545 |
| 147 and 129 | 6321 |
| 23 and 78 | 1794 |
| 66 and 51 | 1122 |