Least Common Multiple (LCM) of 12 and 169
The least common multiple (LCM) of 12 and 169 is 2028.
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 12 and 169?
First, calculate the GCD of 12 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 169 = 0 remainder 12 |
| 2 | 169 ÷ 12 = 14 remainder 1 |
| 3 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 129 | 14577 |
| 194 and 154 | 14938 |
| 143 and 12 | 1716 |
| 159 and 20 | 3180 |
| 100 and 107 | 10700 |