The numbers 14 and 15 are co – prime numbers. How many times is their L.C.M. as compare
to their G.C.D.
Answers
A᭄nswer:-
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Step-by-step explanation:
14 and 15 are coprime (relatively, mutually prime) if they have no common prime factors, that is, if their greatest (highest) common factor (divisor), gcf, hcf, gcd, is 1.
Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd
Approach 1. Integer numbers prime factorization:
Prime Factorization of a number: finding the prime numbers that multiply together to make that number.
14 = 2 × 7;
14 is not a prime, is a composite number;
15 = 3 × 5;
15 is not a prime, is a composite number;
Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.
>> Integer numbers prime factorization
Calculate greatest (highest) common factor (divisor):
Multiply all the common prime factors, by the lowest exponents (if any).
But the two numbers have no common prime factors.
gcf, hcf, gcd (14; 15) = 1;
coprime numbers (relatively prime)
Coprime numbers (relatively prime) (14; 15)? Yes.
Numbers have no common prime factors.
gcf, hcf, gcd (14; 15) = 1.
Approach 2. Euclid's algorithm:
This algorithm involves the operation of dividing and calculating remainders.
'a' and 'b' are the two positive integers, 'a' >= 'b'.
Divide 'a' by 'b' and get the remainder, 'r'.
If 'r' = 0, STOP. 'b' = the GCF (HCF, GCD) of 'a' and 'b'.
Else: Replace ('a' by 'b') & ('b' by 'r'). Return to the division step above.
Step 1. Divide the larger number by the smaller one:
15 ÷ 14 = 1 + 1;
Step 2. Divide the smaller number by the above operation's remainder:
14 ÷ 1 = 14 + 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).
gcf, hcf, gcd (14; 15) = 1;
>> Euclid's algorithm
Coprime numbers (relatively prime) (14; 15)? Yes.
gcf, hcf, gcd (14; 15) = 1.
Final answer:
14 and 15 are coprime (relatively, mutually prime) if they have no common prime factors, that is, if their greatest (highest) common factor (divisor), gcf, hcf, gcd, is 1.
Coprime numbers (relatively prime) (14; 15)? Yes.
gcf, hcf, gcd (14; 15) = 1.
More operations of this kind:
coprime (3,691; 15)? ... (14; 4,759)?
Online calculator: coprime numbers (prime to each other)?
Integer number 1:14
Integer number 2:15