HCF (Highest common factor) :
A common factor is a number that is a factor of two or more other numbers.
The highest common factor (HCF) is the largest factor that is common to two or more numbers.
LCM (Least common Multiple) :
The least common multiple of two or more numbers is the smallest non zero which is a multiple of all numbers.
Find the HCF of LCM of following numbers using prime factorization method :
Problem 1 :
9, 12
Solution :
HCF of (9, 12) = 3
LCM of (9, 12) = 4 x 3^{2} ==> 36
Problem 2 :
8, 16
Solution :
8, 16
HCF of (8, 16) = 2^{3 }==> 8
LCM of (8, 16) = 2^{4} ==> 16
Problem 3 :
18, 42
Solution :
18, 42
HCF of (18, 42) = 3 × 2 ==> 6
LCM of (18, 42) = 3^{2} × 2 x 7 ==> 126
Problem 4 :
14, 42
Solution :
14, 42
HCF of (14, 42) = 2 × 7 ==> 14
LCM of (14, 42) = 2 × 3 x 7 ==> 42
Problem 5 :
18, 30
Solution :
18, 30
HCF of (18, 30) = 3 × 2 ==> 6
LCM of (18, 30) = 3^{2} × 2 x 5 ==> 90
Problem 6 :
24, 32
Solution :
24, 32
HCF of (24, 32) = 2^{3} ==> 8
LCM of (24, 32) = 2^{5 }x 3 ==> 96
Problem 7 :
12, 36
Solution :
12, 36
HCF of (12, 36) = 3 ×
2^{2 }==> 12
LCM of (12, 36) = 3^{2} × 2^{2 } ==> 36
Problem 8 :
15, 33
Solution :
15, 33
HCF of (15, 33) = 3
LCM of (15, 33) = 3 x 11 x 5 ==> 165
Problem 9 :
72, 96
Solution :
72, 96
HCF of (72, 96) = 3 ×
2^{3 }==> 24
LCM of (72, 96) = 3^{2} × 2^{5 }==> 288
Problem 10 :
108, 144
Solution :
108, 144
HCF of (108, 144) = 2^{2} x 3^{2 }==> 36
LCM of (108, 144) = 2^{4} x 3^{3 }==> 432
Problem 11 :
78, 130
Solution :
78, 130
78 = 2 × 3 x 13
130 = 2 × 5 x 13
HCF of (78, 130) ==> 26
LCM of (78, 130) = 2 x 5 x 3 x13 ==> 390
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