H.C.F and L.C.M of Numbers with Explanation

Answer- Option B

Explanation-

	1095 ) 1168 ( 1
	       1095
	       --------------
	       73 ) 1095 ( 15
	              73
	              -------
	              365
	              365
	              
	              ------
	                 x
	              ------   

So, H.C.F. of 1095 and 1168 = 73.

1095 1168

=

1095 + 73 1168 + 73

=

15 16

.

Answer- Option C

Explanation-

The least number divisible by 16, 20, 24
= L.C.M. of 16, 20, 24 = 240 = 2 x 2 x 2 x 2 x 3 x 5.
To make it perfect square, it must be multiplied by 3 x 5.
Required number = 240 x 3 x 5 = 3600.

Answer- Option D

Explanation-

Let the required numbers be 27a and 27b. Then, 27a + 27b = 216
a + b = 8.
Now, co-primes with sum 8 are (1,7) and (3,5).
Required number are (27 x 1, 27 x 7) and (27 x 3, 27 x 5) i.e. (27,189) and (81,135).
Out of these, the given one in the answer is the pair (27,189).

Answer- Option A

Explanation-

204 = 2² x 3 x 17;
1190 = 2 x 5 x 7 x 17;
1445 = 5 x 17².
H.C.F.= 17

Answer- Option C

Explanation-

H.C.F. of two prime numbers is 1. Product of numbers = (1 x 161) = 161.
Let the numbers be p and q. Then, pq = 161.
Now, co-primes with products 161 are (1, 161) and (7, 23).
Since a and b are prime numbers and a > b, we have a = 23 and b = 7.
3b - a = (3 x 7) - 23 = -2.

Answer- Option B

Explanation-

Required number = (L.C.M. of 24, 32, 36, 54) - 5
= 864 - 5 = 859.

Answer- Option A

Explanation-

	3444 ) 3556 ( 1
	       3444
	       --------------
	       112 ) 3444 ( 30
	             3360
	              -------
	             84 )112 ( 3
	                  84  
	                ------
	                  28 ) 84 ( 3
	                       84 
	                      ------
	                         x
	                      ------      

H.C.F. of 3444 and 3556 = 28.