Least Common Multiple (LCM) of 87 and 136
The least common multiple (LCM) of 87 and 136 is 11832.
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 136?
First, calculate the GCD of 87 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 136 = 0 remainder 87 |
| 2 | 136 ÷ 87 = 1 remainder 49 |
| 3 | 87 ÷ 49 = 1 remainder 38 |
| 4 | 49 ÷ 38 = 1 remainder 11 |
| 5 | 38 ÷ 11 = 3 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 42 | 672 |
| 96 and 123 | 3936 |
| 176 and 122 | 10736 |
| 159 and 157 | 24963 |
| 116 and 68 | 1972 |