Least Common Multiple (LCM) of 56 and 87
The least common multiple (LCM) of 56 and 87 is 4872.
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 56 and 87?
First, calculate the GCD of 56 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 87 = 0 remainder 56 |
| 2 | 87 ÷ 56 = 1 remainder 31 |
| 3 | 56 ÷ 31 = 1 remainder 25 |
| 4 | 31 ÷ 25 = 1 remainder 6 |
| 5 | 25 ÷ 6 = 4 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 78 | 1950 |
| 122 and 129 | 15738 |
| 120 and 48 | 240 |
| 142 and 117 | 16614 |
| 110 and 107 | 11770 |