Least Common Multiple (LCM) of 87 and 19
The least common multiple (LCM) of 87 and 19 is 1653.
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 19?
First, calculate the GCD of 87 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 19 = 4 remainder 11 |
| 2 | 19 ÷ 11 = 1 remainder 8 |
| 3 | 11 ÷ 8 = 1 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 20 | 2980 |
| 178 and 180 | 16020 |
| 49 and 165 | 8085 |
| 147 and 127 | 18669 |
| 160 and 141 | 22560 |