Least Common Multiple (LCM) of 14 and 55
The least common multiple (LCM) of 14 and 55 is 770.
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 55?
First, calculate the GCD of 14 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 55 = 0 remainder 14 |
| 2 | 55 ÷ 14 = 3 remainder 13 |
| 3 | 14 ÷ 13 = 1 remainder 1 |
| 4 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 75 | 9600 |
| 70 and 137 | 9590 |
| 147 and 141 | 6909 |
| 68 and 192 | 3264 |
| 116 and 125 | 14500 |