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26.	The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. The sum of the numbers is
	A.  28
	B.  32
	C.  38
	D.  40

Solution

Let the numbers be 2x and 3x. Then, their L.C.M. = 6x. So 6x = 48 or x = 8. Let the numbers are 16 and 24. Required sum = (16 + 24) = 40.

27.	Find the H.C.F. of 108, 288 and 360.
	A.  12
	B.  24
	C.  36
	D.  48

Solution

108 = 22 x 33 288 = 25 x 32 360 = 23 x 5 x 32 Therefore H.C.F. of 22 x 32 = 36.

28.	The H.C.F. of 204, 1190 and 1445 is
	A.  17
	B.  18
	C.  19
	D.  21

Solution

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

29.	The product of the L.C.M. and H.C.F. of two numbers is 24. The difference of two numbers is 2. Find the numbers.
	A.  2 and 4
	B.  6 and 4
	C.  8 and 6
	D.  8 and 10

Solution

Let the numbers be x and (x + 2). Then, x (x + 2) = 24 ‹=›x2 + 2x - 24 = 0 ‹=›(x - 4)(x + 6) = 0 ‹=› x = 4 So, the numbers are 4 and 6.

30.	The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F.?
	A.  8
	B.  12
	C.  35
	D.  48

Solution

Since H.C.F. is always a factor of L.C.M., we cannot have three numbers with H.C.F. 35 and L.C.M. 120.