If p and q are positive integers such that p = a and q= b, where a , b are prime numbers, then the LCM (p, q) is
1 point
a) ab
b) a^2 b^2
c) a^3 b^3
d) a^2 b^3
Answers
Given : p and q are positive integers such that p = a and q= b, where a , b are prime numbers
To Find : LCM (p, q)
a) ab
b) a^2 b^2
c) a^3 b^3
d) a^2 b^3
Solution:
HCF Highest common factor of given numbers is the largest factors which divides all the given numbers perfectly.
HCF = product of common factors of least power
LCM - Least common multiplier of given numbers is the least number which is perfectly divisible by given numbers.
LCM = product of each factor of highest power
HCF ( a, b) * LCM (a , b) = a * b
a , b are prime numbers
Hence HCF ( a, b) = 1
as HCF of 2 different prime numbers is always 1
1 * LCM (a , b) = a * b
=> LCM (a , b) = ab
as p = a and q = b
=> LCM (p , q) = ab
Correct option is a) ab
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Answer:
1 step
p=a , q=b
LCM=p,q
a×b= ab