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 |
|---|---|
| 154 and 154 | 154 |
| 124 and 194 | 12028 |
| 87 and 169 | 14703 |
| 180 and 173 | 31140 |
| 142 and 68 | 4828 |