Least Common Multiple (LCM) of 169 and 116
The least common multiple (LCM) of 169 and 116 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 169 and 116?
First, calculate the GCD of 169 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 116 = 1 remainder 53 |
| 2 | 116 ÷ 53 = 2 remainder 10 |
| 3 | 53 ÷ 10 = 5 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 31 | 1519 |
| 156 and 181 | 28236 |
| 167 and 13 | 2171 |
| 117 and 130 | 1170 |
| 135 and 43 | 5805 |