Least Common Multiple (LCM) of 87 and 47
The least common multiple (LCM) of 87 and 47 is 4089.
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 87 and 47?
First, calculate the GCD of 87 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 47 = 1 remainder 40 |
| 2 | 47 ÷ 40 = 1 remainder 7 |
| 3 | 40 ÷ 7 = 5 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 146 | 20002 |
| 114 and 120 | 2280 |
| 144 and 103 | 14832 |
| 142 and 13 | 1846 |
| 18 and 35 | 630 |