What is the solution to the division problem? Enter numbers in the boxes to complete the problem.
2 answers:
Start with the first number inside the division bracket (4). Because 8 can't go into 4, include the second number in the division bracket (1). Because 8 can go into 41 with a whole number, put a 5 above the bracket and subtract the value of 5*8 from 41. You should get 1. Then, bring down the 6 to form 16. Because 8 can evenly go into 16 twice, put a 2 next to the 5 above the bracket. Multiply 2*8 and subtract the value from 16.
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The LCM of 18 and 24 using the prime-factorization method is <u>72</u>.
The LCM of 27, 81, and 54, using the division method is <u>162</u>.
In the first question, we are asked to find the LCM of the given numbers using the prime factorization method.
(i) 18, 24.
Prime factorization gives:
18 = 2*3², and 24 = 2³*3.
The LCM is the product of the highest power of each prime factor.
Thus, LCM = 2³*3² = 8*9 = 72.
Thus, the LCM of 18 and 24 using the prime-factorization method is <u>72</u>.
Doing similarly for other sub-parts, The LCM of:
(ii) 16, 40 is 80.
(iii) 30, 36 is 180.
(iv) 28, 44 is 308.
(v) 20, 32 is 160.
(vi) 20, 135 is 540.
(vii) 45, 75 is 225.
(viii) 36, 84 is 252.
(ix) 12, 18, 24 is 72.
(x) 25, 35, 45 is 1575.
(xi) 9, 15, 21 is 315.
(xii) 25, 50, 75 is 150.
In the second question, we are asked to find the LCM of the given numbers, using the division method.
(i) 27, 81, 54.
The division method gives:
The LCM is the product of all the numbers used for division.
LCM = 2*3*3*3*3*1 = 162.
Thus, the LCM of 27, 81, and 54, using the division method is <u>162</u>.
Doing similarly for other sub-parts, The LCM of:
(ii) 18, 45, 63 is 630.
(iii) 35, 55, 100 is 7700.
(iv) 210, 140, 315 is 1260.
(v) 112, 120, 150 is 8400.
(vi) 144, 180, 300 is 3600.
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