Least Common Multiple (LCM) of 14 and 151
The least common multiple (LCM) of 14 and 151 is 2114.
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 151?
First, calculate the GCD of 14 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 151 = 0 remainder 14 |
| 2 | 151 ÷ 14 = 10 remainder 11 |
| 3 | 14 ÷ 11 = 1 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 111 | 2220 |
| 190 and 114 | 570 |
| 109 and 166 | 18094 |
| 165 and 111 | 6105 |
| 57 and 144 | 2736 |