Question

LCM & HCP
of 12, 20, 140 using set theory​

Answer 1

Answer:

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Answer 2

Answer:

LCM = 420

HCP = 4

Step-by-step explanation:

let A, B, C be the respective sets of multiples of 12, 20, 140

A = {12, 24, 36, 48,....420, 432,...}

B = { 20, 40, 60, 80,....420, 440,...}

C = { 140, 280, 420,...}

A ∩ B ∩ C = {420, 840,....}

LCM of the numbers is the number with least value in set A intersection B intersection C ⇒ 420

hence, LCM of the numbers 12, 20, 140 is 420

let X, Y, Z be the respective sets of factors of 12, 20, 140

X = { 1, 2, 3, 4, 6, 12}

Y = { 1, 2, 4, 5, 10, 20}

Z = {1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140}

X ∩ Y ∩ Z = {1, 2, 4}

HCF of the numbers is the number with greatest value in the set X intersection Y intersection Z ⇒ 4

hence, HCP of the numbers 12, 20, and 140 is 4