
Least Common Multiple (LCM) of 90 and 31
The least common multiple (LCM) of 90 and 31 is 2790.
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 90 and 31?
First, calculate the GCD of 90 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 90 ÷ 31 = 2 remainder 28 |
2 | 31 ÷ 28 = 1 remainder 3 |
3 | 28 ÷ 3 = 9 remainder 1 |
4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
39 and 55 | 2145 |
193 and 133 | 25669 |
166 and 164 | 13612 |
54 and 88 | 2376 |
23 and 194 | 4462 |