Least Common Multiple (LCM) of 24 and 87
The least common multiple (LCM) of 24 and 87 is 696.
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 24 and 87?
First, calculate the GCD of 24 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 87 = 0 remainder 24 |
| 2 | 87 ÷ 24 = 3 remainder 15 |
| 3 | 24 ÷ 15 = 1 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 49 | 7840 |
| 149 and 127 | 18923 |
| 123 and 113 | 13899 |
| 160 and 41 | 6560 |
| 46 and 172 | 3956 |