
Least Common Multiple (LCM) of 13 and 164
The least common multiple (LCM) of 13 and 164 is 2132.
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 13 and 164?
First, calculate the GCD of 13 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 13 ÷ 164 = 0 remainder 13 |
2 | 164 ÷ 13 = 12 remainder 8 |
3 | 13 ÷ 8 = 1 remainder 5 |
4 | 8 ÷ 5 = 1 remainder 3 |
5 | 5 ÷ 3 = 1 remainder 2 |
6 | 3 ÷ 2 = 1 remainder 1 |
7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
105 and 14 | 210 |
17 and 89 | 1513 |
143 and 65 | 715 |
130 and 93 | 12090 |
98 and 51 | 4998 |