
Least Common Multiple (LCM) of 189 and 71
The least common multiple (LCM) of 189 and 71 is 13419.
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 189 and 71?
First, calculate the GCD of 189 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 189 ÷ 71 = 2 remainder 47 |
2 | 71 ÷ 47 = 1 remainder 24 |
3 | 47 ÷ 24 = 1 remainder 23 |
4 | 24 ÷ 23 = 1 remainder 1 |
5 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
133 and 60 | 7980 |
25 and 133 | 3325 |
120 and 184 | 2760 |
21 and 157 | 3297 |
94 and 53 | 4982 |