Photo AI

2 (a) Find the lowest common multiple (LCM) of 40 and 56 - Edexcel - GCSE Maths - Question 3 - 2018 - Paper 2

Question icon

Question 3

2-(a)-Find-the-lowest-common-multiple-(LCM)-of-40-and-56-Edexcel-GCSE Maths-Question 3-2018-Paper 2.png

2 (a) Find the lowest common multiple (LCM) of 40 and 56. A = 2^3 × 5 B = 2^3 × 3^2 (b) Write down the highest common factor (HCF) of A and B.

Worked Solution & Example Answer:2 (a) Find the lowest common multiple (LCM) of 40 and 56 - Edexcel - GCSE Maths - Question 3 - 2018 - Paper 2

Step 1

Find the lowest common multiple (LCM) of 40 and 56

96%

114 rated

Answer

To find the lowest common multiple (LCM) of 40 and 56, we can start by determining the prime factorization of both numbers:

  • The prime factorization of 40 is: 40=23×540 = 2^3 \times 5
  • The prime factorization of 56 is: 56=23×756 = 2^3 \times 7

To find the LCM, we take the highest power of each prime number from the factorizations:

  • For the prime number 2, the highest power is 232^3.
  • For the prime number 5, the highest power is 515^1.
  • For the prime number 7, the highest power is 717^1.

Thus, the LCM is: LCM=23×51×71=8×5×7=280LCM = 2^3 \times 5^1 \times 7^1 = 8 \times 5 \times 7 = 280

Therefore, the LCM of 40 and 56 is 280.

Step 2

Write down the highest common factor (HCF) of A and B

99%

104 rated

Answer

To find the highest common factor (HCF) of A and B, we use their prime factorizations:

  • For A: A=23×5A = 2^3 \times 5
  • For B: B=23×32B = 2^3 \times 3^2

The HCF is found by taking the lowest power of each common prime factor:

  • For the prime number 2, the lowest power is 232^3.
  • The primes 5 and 3 are not common to both factorizations.

Thus, the HCF is: HCF=23=8HCF = 2^3 = 8

Therefore, the highest common factor (HCF) of A and B is 8.

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;