Question

Find the LCM and HCF of 80, 120, 140 by prime factorization method. ​

Answer 1

Answer:

1. Decompose all numbers into prime factors

80 2 40 2 20 2 10 2 5 5 1 120 2 60 2 30 2 15 3 5 5 1 140 2 70 2 35 5 7 7 1

2. Write all numbers as the product of its prime factors

Prime factors of 80 = 24 . 5

Prime factors of 120 = 23 . 3 . 5

Prime factors of 140 = 22 . 5 . 7

3. Choose the common and uncommon prime factors with the greatest exponent

Common prime factors: 2 , 5

Common prime factors with the greatest exponent: 24, 51

Uncommon prime factors: 3 , 7

Uncommon prime factors with the greatest exponent: 31, 71

4. Calculate the Least Common Multiple or LCM

Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.

LCM = 24. 51. 31. 71 = 1680

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

HCF= 2(80) 2(120) 2(140)

2(40) 2(60) 2(70)

2(20) 2(30). 5(35)

2(10) 3(15) 7

5. 5

80=2,2,2,2,5

120=2,2,2,3,5

140=2,2,5,7

Common factor= 2,2,4

2×2×4=16

HCF=16

2. LCM= 80×120×140= 5600

60

LCM=5600