Find which of the following pairs of numbers are co-primes.
1) 4 and 12.
2) 7 and 43.
3) 5 and 3.
4) 8 and 17.
5) 8 and 15.
6) 14 and 21.
7) 2 and 4.
8) 1 and 2.
9) If the product of two co-prime numbers is 345, find the LCM of the numbers.
10) The LCM of two co-prime numbers is 420. If one of the numbers is 15, then find the other number.
Answer (1) :
4 and 12 have the common divisors other than 1.
They are 2 and 4.
So, 4 and 12 are not co-primes.
Answer (2)
7 and 43 have no common divisor other than 1.
So, 7 and 43 are co-primes.
Answer (3) :
5 and 3 have no common divisor other than 1.
So, 5 and 3 are co-primes.
Answer (4) :
8 and 17 have no common divisor other than 1.
So, 8 and 17 are co-primes.
Answer (5) :
8 and 15 have no common divisor other than 1.
So, 8 and 15 are co-primes.
Answer (6) :
14 and 21 have common divisor other than 1.
That is 7.
So, 14 and 21 are not co-primes.
Answer (7) :
2 and 4 have common divisor other than 1.
That is 2.
So, 2 and 4 are not co-primes.
Answer (8) :
1 and 2 have no common divisor other than 1.
So, 1 and 2 are co-primes.
Answer (9) :
Because the two numbers are co-prime, their HCF is 1.
We know that,
LCM x HCF = Product of the two numbers
Substitute.
LCM x 1 = 345
LCM = 345
Answer (10) :
Let x be the other number.
We know that,
Product of the two numbers = LCM x HCF
As the HCF of co-primes is 1,
15(x) = 420 x 1
15x = 420
Divide each side by 15.
x = 28
The other number is 28.
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