Least Common Multiple (LCM) of 87 and 64
The least common multiple (LCM) of 87 and 64 is 5568.
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 64?
First, calculate the GCD of 87 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 64 = 1 remainder 23 |
| 2 | 64 ÷ 23 = 2 remainder 18 |
| 3 | 23 ÷ 18 = 1 remainder 5 |
| 4 | 18 ÷ 5 = 3 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 114 | 3192 |
| 62 and 70 | 2170 |
| 109 and 71 | 7739 |
| 30 and 98 | 1470 |
| 183 and 64 | 11712 |