and 5
Find the LCM and HCF of the following integers by applying the prime
12.15 und 21
(11) 17,23 and 29
(1) 8.9 and 25
Answers
Heya friend... here you go with your amazing answer...
(i) GIVEN: 15, 12 and 21
The prime factors of 15, 12 and 21 are :
12 = 2 x 2 x 3 = 2² × 3¹
15 = 3 x 5 = 3¹ × 5¹
21 = 3 x 7 = 3¹ × 7¹
L.C.M of 12, 15 and 21 =2² × 3¹ × 5¹ × 7¹ = 2 x 2 x 3 x 5 x 7 = 420
L.C.M of 12, 15 and 21 = 420
[LCM of two or more numbers = product of the greatest power of each prime factor involved in the numbers, with highest power.]
H.C.F of 12, 15 and 21 = 3
[HCF(Highest Common Factor) of two or more numbers= Product of the smallest Power of each common prime factor involved in the numbers.]
Hence, H.C.F( 12, 15 and 21) = 3 & L.C.M (12, 15 and 21) 420.
(ii) GIVEN : 17, 23 and 29
The prime factors of 17, 23 and 29 are:
17 = 1 x 17
23 = 1 x 23
29 = 1 x 29
L.C.M of 17, 23 and 29 = 1 x 17 x 23 x 29
L.C.M of 17, 23 and 29 = 11339
[LCM of two or more numbers = product of the greatest power of each prime factor involved in the numbers, with highest power.]
H.C.F of 17, 23 and 29 = 1
[HCF(Highest Common Factor) of two or more numbers= Product of the smallest Power of each common prime factor involved in the numbers.]
Hence, H.C.F( 17, 23 and 29) & L.C.M (17, 23 and 2) = 11339.
(iii) GIVEN : 8, 9 and 25
The prime factors of 8, 9 and 25 are :
8 = 2 x 2 x2 = 2³
9 = 3 x 3 = 3²
25 = 5 x 5 = 5²
L.C.M of 8, 9 and 25 = 2³ x 3² x 5² = 2 x 2 x2 × 3 x 3 × 5 x 5
L.C.M of 8, 9 and 25 = 1800
[LCM of two or more numbers = product of the greatest power of each prime factor involved in the numbers, with highest power.]
H.C.F of 8, 9 and 25 = 1
[HCF(Highest Common Factor) of two or more numbers= Product of the smallest Power of each common prime factor involved in the numbers.]
Hence, H.C.F(8, 9 and 25) = 1 & L.C.M (8, 9 and 25 ) = 1800.
have a great day mate!!!
Answer:
hcf 3 lcm 420 ( first one)
hcf 1 lcm 11339 ( second one)
hcf 1 lcm 1800 ( third one)