
Least Common Multiple (LCM) of 199 and 144
The least common multiple (LCM) of 199 and 144 is 28656.
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 199 and 144?
First, calculate the GCD of 199 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 199 ÷ 144 = 1 remainder 55 |
2 | 144 ÷ 55 = 2 remainder 34 |
3 | 55 ÷ 34 = 1 remainder 21 |
4 | 34 ÷ 21 = 1 remainder 13 |
5 | 21 ÷ 13 = 1 remainder 8 |
6 | 13 ÷ 8 = 1 remainder 5 |
7 | 8 ÷ 5 = 1 remainder 3 |
8 | 5 ÷ 3 = 1 remainder 2 |
9 | 3 ÷ 2 = 1 remainder 1 |
10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
103 and 159 | 16377 |
133 and 61 | 8113 |
49 and 96 | 4704 |
51 and 24 | 408 |
75 and 39 | 975 |