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 |
|---|---|
| 137 and 96 | 13152 |
| 96 and 197 | 18912 |
| 47 and 113 | 5311 |
| 188 and 65 | 12220 |
| 160 and 95 | 3040 |