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# The least common multiple of positive integers p and q is 630. if the

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Re: The least common multiple of positive integers p and q is 630. if the [#permalink]
­LCM = 630
GCD = 18
=> P * Q = 630 * 18

(1) P is multiple of 35

630 = 70 * 6 = 35 * 12

P can be
• 35
• 70 = 35 * 2
• 105 = 35 * 3
• 140 = 35 * 4
• 210 = 35 * 6
• 630 = 35 * 12
Only 630 can be divisible by 18
=> P = 630
=> Q = 18

=> Sufficient

(2) GCD of Q and 35 is 1
630 = 35 * 12
=> P must be divisible by 35
Similar as in case 1 => Sufficient

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Re: The least common multiple of positive integers p and q is 630. if the [#permalink]
Given: The least common multiple of positive integers p and q is 630.
Asked: If the greatest common factor of P and Q is 18, what is P - Q?
PQ = LCM(P,Q)*GCF(P,Q) = 630*18 =  2^2*3^4*5*7
Case 1: P = 630; Q=18; P-Q = 612
Case 2: P = 18; Q=630; P-Q = -612
Case 3: P= 90; Q = 126; P-Q = -36
Case 4: P= 126; Q = 90; P-Q = 36

(1) P is a multiple of 35
P=630; Q=18; P-Q=612
SUFFICIENT

(2) The GCD of Q and 35 is 1Q=18; P=630; P-Q=612
SUFFICIENT

IMO D
­
Re: The least common multiple of positive integers p and q is 630. if the [#permalink]
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