Question

11/6358 long agurithum

Answer 1

Answer:

Least common multiple:

lcm (578; 11) = 6,358 = 2 × 11 × 172;

Numbers have no common prime factors: 6,358 = 578 × 11.

Step-by-step 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;