Least Common Multiple (LCM) of 87 and 119
The least common multiple (LCM) of 87 and 119 is 10353.
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 119?
First, calculate the GCD of 87 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 119 = 0 remainder 87 |
| 2 | 119 ÷ 87 = 1 remainder 32 |
| 3 | 87 ÷ 32 = 2 remainder 23 |
| 4 | 32 ÷ 23 = 1 remainder 9 |
| 5 | 23 ÷ 9 = 2 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 20 | 720 |
| 74 and 110 | 4070 |
| 76 and 55 | 4180 |
| 84 and 111 | 3108 |
| 193 and 107 | 20651 |