Q6. Find the LCM of 30, 40 ?
A. As we know
Prime Factorization of 30 = 21 * 31 * 51
Prime Factorization of 40 = 23 * 51
So, As we learned in our tutorial , we know that the least number that can be divided by each one of the numbers is LCM.
HCF = 23 * 31 * 51 => 120
Q7. Find the LCM of 72, 108, 2100 ?
A. As we know
Prime Factorization of 72 = 23 * 32 …1
Prime Factorization of 108 = 22 * 33 …2
Prime Factorization of 2100 = 22 * 31 * 52 * 71 …3
Let us find the HCF of eq.1 & eq.2 :
HCF12 = 23 * 33 => 216 …4
Let us find the HCF of eq.3 & eq.4 :
HCF34 = 23 * 33 * 52 * 71=> 37800
Q8. Find the LCM of x, y, z such that their prime factorization are :
x => 23 * 51 * 71 * 112
y => 21 * 31 * 51
z => 22 * 32 * 52 * 112
A. LCM = Product of highest powers :
So, answer is :
23 * 32 * 52 * 112
Q9. Find the LCM of 36, 48 ?
A. As we know
Prime Factorization of 36 = 22 * 32
Prime Factorization of 48 = 24 * 31
So, LCM : 24 * 32 => 144
Q10. Find the LCM of 0.63, 1.05, and .21 ?
A. If we consider, the above numbers without decimal, so updated numbers will be 63, 105, 210.
Prime Factorization of 63 = 32 * 71 …1
Prime Factorization of 105 = 31 * 51 * 71 …2
Prime Factorization of 21 = 31 * 71 …3
Let us find the LCM of eq.1 & eq.2 :
LCM12 = 32 * 51 * 71 => 315 …4
Let us find the HCF of eq.3 & eq.4 :
HCF34 = 32 * 51 * 71 => 315
So, it can be converted to its original form : 3.15