Least Common Multiple (LCM) of 105 and 119
The least common multiple (LCM) of 105 and 119 is 1785.
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 105 and 119?
First, calculate the GCD of 105 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 119 = 0 remainder 105 |
| 2 | 119 ÷ 105 = 1 remainder 14 |
| 3 | 105 ÷ 14 = 7 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 107 | 20544 |
| 141 and 129 | 6063 |
| 103 and 139 | 14317 |
| 77 and 50 | 3850 |
| 32 and 36 | 288 |