Least Common Multiple (LCM) of 101 and 119
The least common multiple (LCM) of 101 and 119 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 101 and 119?
First, calculate the GCD of 101 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 119 = 0 remainder 101 |
| 2 | 119 ÷ 101 = 1 remainder 18 |
| 3 | 101 ÷ 18 = 5 remainder 11 |
| 4 | 18 ÷ 11 = 1 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 164 | 10988 |
| 123 and 193 | 23739 |
| 109 and 34 | 3706 |
| 143 and 21 | 3003 |
| 130 and 197 | 25610 |