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LCM

by artstudent » Mon Jul 25, 2011 6:59 pm
The least common multiple of positive integer m and 3-digit integer n is 690. If n is not divisible by 3 and m is not divisible by 2, what is
the value of n?

A. 115
B. 230
C. 460
D. 575
E. 690
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by winniethepooh » Mon Jul 25, 2011 7:51 pm
The answer is 230.
It is given that n is a three digit integer and not divisible by 3. the LCM of N and another positive integer is 690.

Factors= 2*3*5*23= 690

Answer choice 1:
690 is a multiple but if you check the factors the remaining factors give a multiple of 2.(not the answer as M can't be divicible by 2.

Answer choice 2:
230(Satisfies all conditions)(on hold, check others)

Answer choice 3:
690 is not a multiple.

Answer choice 4:
690 not a multiple

Answer choice 5:
690 (multiple of 690 but also divisible by 3)(Does not work)

Hence, correct answer is 2: 230.
Last edited by winniethepooh on Mon Jul 25, 2011 8:39 pm, edited 1 time in total.
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by atuljadhav » Mon Jul 25, 2011 8:20 pm
The common factors should be other than 2 and 3. Could be 5,7,11 etc,.

Lets factor every number and see the common factors.

Only 575 has factors of 5 and 23.
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