Least Common Multiple (LCM) of 14 and 169
The least common multiple (LCM) of 14 and 169 is 2366.
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 14 and 169?
First, calculate the GCD of 14 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 169 = 0 remainder 14 |
| 2 | 169 ÷ 14 = 12 remainder 1 |
| 3 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 153 | 6273 |
| 130 and 167 | 21710 |
| 31 and 82 | 2542 |
| 137 and 132 | 18084 |
| 140 and 51 | 7140 |