Least Common Multiple (LCM) of 169 and 104
The least common multiple (LCM) of 169 and 104 is 1352.
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 104?
First, calculate the GCD of 169 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 104 = 1 remainder 65 |
| 2 | 104 ÷ 65 = 1 remainder 39 |
| 3 | 65 ÷ 39 = 1 remainder 26 |
| 4 | 39 ÷ 26 = 1 remainder 13 |
| 5 | 26 ÷ 13 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 100 | 300 |
| 143 and 14 | 2002 |
| 119 and 64 | 7616 |
| 107 and 13 | 1391 |
| 110 and 197 | 21670 |