
Least Common Multiple (LCM) of 90 and 56
The least common multiple (LCM) of 90 and 56 is 2520.
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 56?
First, calculate the GCD of 90 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 90 ÷ 56 = 1 remainder 34 |
2 | 56 ÷ 34 = 1 remainder 22 |
3 | 34 ÷ 22 = 1 remainder 12 |
4 | 22 ÷ 12 = 1 remainder 10 |
5 | 12 ÷ 10 = 1 remainder 2 |
6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
110 and 181 | 19910 |
175 and 100 | 700 |
169 and 12 | 2028 |
170 and 173 | 29410 |
31 and 77 | 2387 |