Least Common Multiple (LCM) of 119 and 87
The least common multiple (LCM) of 119 and 87 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 119 and 87?
First, calculate the GCD of 119 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 87 = 1 remainder 32 |
| 2 | 87 ÷ 32 = 2 remainder 23 |
| 3 | 32 ÷ 23 = 1 remainder 9 |
| 4 | 23 ÷ 9 = 2 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 170 | 8330 |
| 62 and 139 | 8618 |
| 164 and 180 | 7380 |
| 106 and 128 | 6784 |
| 116 and 40 | 1160 |