
Least Common Multiple (LCM) of 100 and 174
The least common multiple (LCM) of 100 and 174 is 8700.
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 174?
First, calculate the GCD of 100 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 100 ÷ 174 = 0 remainder 100 |
2 | 174 ÷ 100 = 1 remainder 74 |
3 | 100 ÷ 74 = 1 remainder 26 |
4 | 74 ÷ 26 = 2 remainder 22 |
5 | 26 ÷ 22 = 1 remainder 4 |
6 | 22 ÷ 4 = 5 remainder 2 |
7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
12 and 185 | 2220 |
61 and 91 | 5551 |
144 and 11 | 1584 |
54 and 121 | 6534 |
197 and 18 | 3546 |