Least Common Multiple (LCM) of 119 and 101
The least common multiple (LCM) of 119 and 101 is 12019.
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 101?
First, calculate the GCD of 119 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 101 = 1 remainder 18 |
| 2 | 101 ÷ 18 = 5 remainder 11 |
| 3 | 18 ÷ 11 = 1 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 193 | 23160 |
| 115 and 164 | 18860 |
| 122 and 138 | 8418 |
| 11 and 177 | 1947 |
| 107 and 53 | 5671 |