EXERCISE - 5.8
1. Find the LCM of the following numbers by prime factorization m
(a) 36 and 45
(b) 24 and 40 (c) 32 and
(d) 70 and 92
(e) 63 and 105 () 58 and 4
(g) 48 and 72
(h) 28 and 84
() 110 and 1
Find the LCM of the following numbers by common division me
(a) 25 and 30
(b) 32 and 48 (c) 42 and 7
(d) 72 and 96
(e) 42 and 70 b) 42 and
) 10,135 and 150 (h) 102,136 and 170 @ 255,340
Find the HCF and LCM of the following numbers:
() 87 and 145 ) 161 and 201 270 and
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(A)The prime factorization of 36 is: 2 x 2 x 3 x 3
The prime factorization of 45 is: 3 x 3 x 5
Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(36,36) = 180
(B) prime factorization of 24
24 = 2 × 2 × 2 × 3
prime factorization of 40
40 = 2 × 2 × 2 × 5
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2 × 2 × 2 × 3 × 5
LCM = 120
C) prime factorization of 70
70 = 2 × 5 × 7
prime factorization of 92
92 = 2 × 2 × 23
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2 × 2 × 5 × 7 × 23
LCM = 3220
E)prime factorization of 63
63 = 3 × 3 × 7
Find the prime factorization of 105
105 = 3 × 5 × 7
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3 × 3 × 5 × 7
LCM = 315
F) The multiples of 58 are … , 58, 116, 174, ….
The multiples of 4 are …, 112, 116, 120, …
The common multiples of 58 and 4 are n x 116, intersecting the two sets above, .
In the intersection multiples of 58 ∩ multiples of 4 the least positive element is 116.
Therefore, the least common multiple of 58 and 4 is 116.
G) The multiples of 48 are … , 96, 144, 192, ….
The multiples of 72 are …, 72, 144, 216, …
The common multiples of 48 and 72 are n x 144, intersecting the two sets above, .
In the intersection multiples of 48 ∩ multiples of 72 the least positive element is 144.
Therefore, the least common multiple of 48 and 72 is 144.
H) prime factorization of 28
28 = 2 × 2 × 7
prime factorization of 84
84 = 2 × 2 × 3 × 7
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2 × 2 × 3 × 7
LCM = 84
The prime factorization of 45 is: 3 x 3 x 5
Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(36,36) = 180
(B) prime factorization of 24
24 = 2 × 2 × 2 × 3
prime factorization of 40
40 = 2 × 2 × 2 × 5
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2 × 2 × 2 × 3 × 5
LCM = 120
C) prime factorization of 70
70 = 2 × 5 × 7
prime factorization of 92
92 = 2 × 2 × 23
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2 × 2 × 5 × 7 × 23
LCM = 3220
E)prime factorization of 63
63 = 3 × 3 × 7
Find the prime factorization of 105
105 = 3 × 5 × 7
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3 × 3 × 5 × 7
LCM = 315
F) The multiples of 58 are … , 58, 116, 174, ….
The multiples of 4 are …, 112, 116, 120, …
The common multiples of 58 and 4 are n x 116, intersecting the two sets above, .
In the intersection multiples of 58 ∩ multiples of 4 the least positive element is 116.
Therefore, the least common multiple of 58 and 4 is 116.
G) The multiples of 48 are … , 96, 144, 192, ….
The multiples of 72 are …, 72, 144, 216, …
The common multiples of 48 and 72 are n x 144, intersecting the two sets above, .
In the intersection multiples of 48 ∩ multiples of 72 the least positive element is 144.
Therefore, the least common multiple of 48 and 72 is 144.
H) prime factorization of 28
28 = 2 × 2 × 7
prime factorization of 84
84 = 2 × 2 × 3 × 7
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2 × 2 × 3 × 7
LCM = 84
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