Answer:
Least common multiple:
lcm (578; 11) = 6,358 = 2 × 11 × 172;
Numbers have no common prime factors: 6,358 = 578 × 11.
Explanation:
Approach 1. Integer numbers prime factorization:
578 = 2 × 172;
11 is a prime number, it cannot be broken down to other prime factors;
Multiply all the prime factors, by the largest exponents.
Least common multiple:
lcm (578; 11) = 2 × 11 × 172;
lcm (578; 11) = 2 × 11 × 172 = 6,358
Numbers have no common prime factors: 6,358 = 578 × 11.
Integer numbers prime factorization
Approach 2. Euclid's algorithm:
Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:
Step 1. Divide the larger number by the smaller one:
578 ÷ 11 = 52 + 6; Step 2. Divide the smaller number by the above operation's remainder:
11 ÷ 6 = 1 + 5; Step 3. Divide the remainder from the step 1 by the remainder from the step 2:
6 ÷ 5 = 1 + 1; Step 4. Divide the remainder from the step 2 by the remainder from the step 3:
5 ÷ 1 = 5 + 0; At this step, the remainder is zero, so we stop:
1 is the number we were looking for, the last remainder that is not zero.
This is the greatest common factor (divisor).
Least common multiple, formula:
lcm (a; b) = (a × b) / gcf, hcf, gcd (a; b);
lcm (578; 11) =
(578 × 11) / gcf, hcf, gcd (578; 11) =
6,358 / 1 =
6,358;
lcm (578; 11) = 6,358 = 2 × 11 × 172;