Answered

The prime factor decompositions of two numbers, T and X, are shown below.

T 2^5x 3^8x 5

X = 2^4x 3^2 × 5 × 7

Work out the

a) lowest common multiple (LCM) of T and X.

b) highest common factor (HCF) of T and X.

Give your answers as products of their prime factors in index form



Answer :

Answer:

Step-by-step explanation:

Lowest Common Multiple (LCM) of T and X:

First, let’s find the prime factorization of both T and X:

T: 25⋅38⋅5

X: 24⋅32⋅5⋅7

Now, identify the common prime factors and their highest powers:

Common factors: 24

and 32

Highest power of 2: 24

(from X)

Highest power of 3: 32

(from X)

Highest power of 5: 5

(from both T and X)

Highest power of 7: 7

(from X)

Multiply these highest powers together:

LCM = 24⋅32⋅5⋅7=2520

Highest Common Factor (HCF) of T and X:

The HCF is found by multiplying the common prime factors with their lowest powers:

Common factors: 24

and 32

Lowest power of 2: 24

(from T)

Lowest power of 3: 32

(from T)

HCF = 24⋅32=144

Therefore:

LCM of T and X = 2520

HCF of T and X = 144

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