Least Common Multiple (LCM) of 14 and 120
The least common multiple (LCM) of 14 and 120 is 840.
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 120?
First, calculate the GCD of 14 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 120 = 0 remainder 14 |
| 2 | 120 ÷ 14 = 8 remainder 8 |
| 3 | 14 ÷ 8 = 1 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 59 | 6785 |
| 22 and 78 | 858 |
| 22 and 139 | 3058 |
| 49 and 157 | 7693 |
| 151 and 107 | 16157 |