Least Common Multiple (LCM) of 14 and 87
The least common multiple (LCM) of 14 and 87 is 1218.
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 87?
First, calculate the GCD of 14 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 87 = 0 remainder 14 |
| 2 | 87 ÷ 14 = 6 remainder 3 |
| 3 | 14 ÷ 3 = 4 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 165 | 1155 |
| 159 and 37 | 5883 |
| 115 and 91 | 10465 |
| 57 and 86 | 4902 |
| 16 and 130 | 1040 |