Question

find the HCF and LCM of 1376 and 15428 by applying prime factorazation

Answer 1

1,376 = 25 × 43; 
15,428 = 22 × 7 × 19 × 29;

lcm (1,376; 15,428) = 25 × 7 × 19 × 29 × 43 = 5,307,232


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Calculate the least common multiple of numbers, LCM (1,376; 15,428)

lcm (1,376; 15,428) = 5,307,232; 
Numbers have common prime factors.

Approach 1. Integer numbers prime factorization. Approach 2. Euclid's algorithm. Explanations below.

Approach 1. Integer numbers prime factorization:

1,376 = 25 × 43; 
15,428 = 22 × 7 × 19 × 29;

Take all the prime factors, by the largest powers (exponents).

Least common multiple 
lcm (1,376; 15,428) = 25 × 7 × 19 × 29 × 43 = 5,307,232;

Approach 2. Euclid's algorithm:

Calculate the greatest (highest) common factor (divisor), gcf, gcd:

Step 1. Divide the larger number by the smaller one: 
15,428 ÷ 1,376 = 11 + 292;

Step 2. Divide the smaller number by the above operation's remainder: 
1,376 ÷ 292 = 4 + 208;Step 3. Divide the remainder from the step 1 by the remainder from the step 2: 
292 ÷ 208 = 1 + 84;Step 4. Divide the remainder from the step 2 by the remainder from the step 3: 
208 ÷ 84 = 2 + 40;Step 5. Divide the remainder from the step 3 by the remainder from the step 4: 
84 ÷ 40 = 2 + 4;Step 6. Divide the remainder from the step 4 by the remainder from the step 5: 
40 ÷ 4 = 10 + 0;At this step, the remainder is zero, so we stop: 
4 is the number we were looking for, the last remainder that is not zero. 
This is the greatest common factor (divisor).

Least common multiple, lcm:
lcm (a; b) = (a × b) / gcf, gcd (a; b);

lcm (1,376; 15,428) = (1,376 × 15,428) / gcf, gcd (1,376; 15,428) = 21,228,928 / 4 = 5,307,232;

Least common multiple 
lcm (1,376; 15,428) = 5,307,232 = 25 × 7 × 19 × 29 × 43;

Answer 2

1,376= 25×43;
15,428 = 22×7 × 19 ×29
LCM=( 1376;15428) = 25 ×7 ×19×29
43=5,307, 232