Least Common Multiple (LCM) of 100 and 55
The least common multiple (LCM) of 100 and 55 is 1100.
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 100 and 55?
First, calculate the GCD of 100 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 55 = 1 remainder 45 |
| 2 | 55 ÷ 45 = 1 remainder 10 |
| 3 | 45 ÷ 10 = 4 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 141 | 6768 |
| 111 and 57 | 2109 |
| 106 and 113 | 11978 |
| 79 and 72 | 5688 |
| 34 and 32 | 544 |