
Least Common Multiple (LCM) of 165 and 106
The least common multiple (LCM) of 165 and 106 is 17490.
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 165 and 106?
First, calculate the GCD of 165 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 165 ÷ 106 = 1 remainder 59 |
2 | 106 ÷ 59 = 1 remainder 47 |
3 | 59 ÷ 47 = 1 remainder 12 |
4 | 47 ÷ 12 = 3 remainder 11 |
5 | 12 ÷ 11 = 1 remainder 1 |
6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
133 and 100 | 13300 |
94 and 29 | 2726 |
164 and 189 | 30996 |
145 and 120 | 3480 |
163 and 122 | 19886 |