Least Common Multiple (LCM) of 43 and 119
The least common multiple (LCM) of 43 and 119 is 5117.
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 43 and 119?
First, calculate the GCD of 43 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 119 = 0 remainder 43 |
| 2 | 119 ÷ 43 = 2 remainder 33 |
| 3 | 43 ÷ 33 = 1 remainder 10 |
| 4 | 33 ÷ 10 = 3 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 151 | 17063 |
| 67 and 159 | 10653 |
| 146 and 102 | 7446 |
| 10 and 67 | 670 |
| 134 and 18 | 1206 |