Lcm = 22 + gcd

The least common multiple of two numbers is 22 more than their greatest common divisor. Find these numbers.

Correct answer:

a =  5

Step-by-step explanation:

a1=8;b1=6 a2=23;b2=1 a3=24;b3=2 a4=33;b4=11 a5=44;b5=22 a=5  8=23 6=23 GCD(8,6)=2  d1=GCD(8,6)=2  8=23 6=23 LCM(8,6)=233=24  n1=LCM(8,6)=24 d1+22=n1 23 ...  prime number 1 ...  prime number GCD(23,1)=1  d2=GCD(23,1)=1  23 ...  prime number 1 ...  prime number LCM(23,1)=23  n2=LCM(23,1)=23 d2+22=n2 24=233 2 ...  prime number GCD(24,2)=2  d3=GCD(24,2)=2  24=233 2 ...  prime number LCM(24,2)=233=24  n3=LCM(24,2)=24 d3+22=n3 33=311 11 ...  prime number GCD(33,11)=11  d4=GCD(33,11)=11  33=311 11 ...  prime number LCM(33,11)=311=33  n4=LCM(33,11)=33 d4+22=n4 44=2211 22=211 GCD(44,22)=211=22  d5=GCD(44,22)=22  44=2211 22=211 LCM(44,22)=2211=44  n5=LCM(44,22)=44 d5+22=n5

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