
Least Common Multiple (LCM) of 83 and 128
The least common multiple (LCM) of 83 and 128 is 10624.
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 83 and 128?
First, calculate the GCD of 83 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 83 ÷ 128 = 0 remainder 83 |
2 | 128 ÷ 83 = 1 remainder 45 |
3 | 83 ÷ 45 = 1 remainder 38 |
4 | 45 ÷ 38 = 1 remainder 7 |
5 | 38 ÷ 7 = 5 remainder 3 |
6 | 7 ÷ 3 = 2 remainder 1 |
7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
119 and 128 | 15232 |
200 and 37 | 7400 |
150 and 82 | 6150 |
54 and 127 | 6858 |
111 and 99 | 3663 |