Least Common Multiple (LCM) of 144 and 87
The least common multiple (LCM) of 144 and 87 is 4176.
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 144 and 87?
First, calculate the GCD of 144 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 87 = 1 remainder 57 |
| 2 | 87 ÷ 57 = 1 remainder 30 |
| 3 | 57 ÷ 30 = 1 remainder 27 |
| 4 | 30 ÷ 27 = 1 remainder 3 |
| 5 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 117 | 13104 |
| 82 and 85 | 6970 |
| 114 and 164 | 9348 |
| 59 and 137 | 8083 |
| 106 and 25 | 2650 |